Spatio-temporal processing for communication

ABSTRACT

A space-time signal processing system with advantageously reduced complexity. The system may take advantage of multiple transmitter antenna elements and/or multiple receiver antenna elements, or multiple polarizations of a single transmitter antenna element and/or single receiver antenna element. The system is not restricted to wireless contexts and may exploit any channel having multiple inputs or multiple outputs and certain other characteristics. Multi-path effects in a transmission medium cause a multiplicative increase in capacity.

STATEMENT OF RELATED APPLICATIONS

[0001] The present application claims priority from two provisionalapplications: SPATIO-TEMPORAL CODING FOR WIRELESS COMMUNICATION, U.S.Prov. App. No. 60/025,227 and SPATIO-TEMPORAL CODING TECHNIQUES FORRAPIDLY FADING WIRELESS CHANNELS, U.S. Prov. App. No. 60/025,228, bothfiled on Aug. 29, 1996. The contents of both provisional applicationsare herein incorporated by reference for all purposes.

BACKGROUND OF THE INVENTION

[0002] The present invention relates to digital communication and moreparticularly to a space-time communication system.

[0003] The ability to communicate through wireless media is madedifficult by the inherent characteristics of how transmitted signalspropagate through the environment. A communication signal transmittedthrough a transmitter antenna element travels along multiple paths tothe receiving antenna element. Depending on many factors including thesignal frequency and the terrain, the paths along which the signaltravels will exhibit different attenuation and propagation delays. Thisresults in a communication channel which exhibits fading and delayspread.

[0004] It is well known that adaptive spatial processing using multipleantenna arrays increases the communications quality of wireless systems.Adaptive array processing is known to improve bit error rate, data rate,or spectral efficiency in a wireless communication system. The prior artprovides for methods involving some form of space-time signal processingat either the input to the channel, the output to the channel, or both.The space-time processing step is typically accomplished using anequalization structure wherein the time domain equalizer tap settingsfor a multitude of antennas are simultaneously optimized. This so-called“space-time equalizaion” leads to high signal processing complexity ifthe delay spread of the equivalent digital channel is substantial.

[0005] There is prior art teaching the use of conventional antenna beamsor polarizations to create two or more spatially isolated communicationchannels between a transmitter and a receiver, but only under certainfavorable conditions. The radiation pattern cross talk between differentphysical transmit and receive antenna pairs must provide sufficientspatial isolation to create two or more substantially independentcommunication channels. This can lead to stringent manufacturing andperformance requirements on the physical antenna arrays as well as thereceiver and transmitter electronics. In addition, when large objects inthe wireless propagation channel cause multipath reflections, thespatial isolation provided by the prior art between any two spatialsubchannels can be severely degraded, thus reducing communicationquality.

[0006] What is needed is a system for more effectively taking advantageof multiple transmitter antennas and/or multiple receiver antennas toameliorate the deleterious effects of the inherent characteristics ofwireless media.

SUMMARY OF THE INVENTION

[0007] The present invention provides a space-time signal processingsystem with advantageously reduced complexity. The system may takeadvantage of multiple transmitter antenna elements and/or multiplereceiver antenna elements, or multiple polarizations of a singletransmitter antenna element and/or single receiver antenna element. Thesystem is not restricted to wireless contexts and may exploit anychannel having multiple inputs or multiple outputs and certain othercharacteristics. In certain embodiments, multi-path effects in atransmission medium cause a multiplicative increase in capacity.

[0008] One wireless embodiment operates with an efficient combination ofa substantially orthogonalizing procedure (SOP) in conjunction with aplurality of transmitter antenna elements with one receiver antennaelement, or a plurality of receiver antenna elements with one transmitantenna element, or a pluraltiy of both transmitter and receiver antennaelements. The SOP decomposes the time domain space-time communicationchannel that may have inter symbol interference (ISI) into a set ofparallel, space-frequency, SOP bins wherein the ISI is substantiallyreduced and the signal received at a receiver in one bin of the SOP issubstantially independent of the signal received in any other bin of theSOP. A major benefit achieved thereby is that the decomposition of theISI-rich space time channel into substantially independent SOP binsmakes it computationally efficient to implement various advantageousspatial processing techniques embodied herein. The efficiency benefit isdue to the fact that the total signal processing complexity required tooptimize performance in all of the SOP bins is often significantly lowerthan the processing complexity required to jointly optimize multipletime domain equalizers.

[0009] Another benefit is that in many types of wireless channels wherethe rank of the matrix channel that exist between the transmitter andthe receiver within each SOP bin is greater than one, the combination ofan SOP with spatial processing can be used to efficiently providemultiple data communication subchannels within each SOP bin. This hasthe desirable effect of essentially multiplying the spectral dataefficiency of the wireless system. A further feature is the use ofspatial processing techniques within each transmitter SOP bin to reduceradiated interference to unintentional receivers. A still furtherfeature is the ability to perform spatial processing within eachreceiver SOP bin to reduce the deleterious effects of interference fromunintentional transmitters.

[0010] One advantageous specific embodiment for the SOP is to transmitwith IFFT basis functions and receive with FFT basis functions. Thisparticular SOP is commonly referred to as discrete orthogonal frequencydivision multiplexing (OFDM), and each SOP bin is thus associated with afrequency bin. This embodiment enhances OFDM with the addition ofefficient spatial processing techniques.

[0011] According to the present invention, space-frequency processingmay adaptively create substantially independent spatial subchannelswithin each SOP bin even in the presence of significant cross talkinterference between two or more physical transmit and receive antennapairs. A further advantage is that the space-frequency processing canadvantageously adapt to cross talk interference between the physicalantenna pairs even if this cross-talk is frequency dependent, or timevarying, or both. Thus, the present invention may provide two or moresubstantially independent communication channels even in the presence ofsevere multipath and relatively poor physical antenna radiation patternperformance.

[0012] A further understanding of the nature and advantages of theinventions herein may be realized by reference to the remaining portionsof the specification and the attached drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

[0013]FIG. 1 depicts a transmitter system according to one embodiment ofthe present invention.

[0014]FIG. 2 depicts a particular substantial orthogonalizing procedure(SOP) useful in one embodiment of the present invention.

[0015]FIG. 3 depicts a receiver system according to one embodiment ofthe present invention.

[0016]FIG. 4 depicts a first communication scenario where multipath isfound.

[0017]FIG. 5 depicts a second communication scenario where multipath isfound.

[0018]FIG. 6 depicts a third communication scenario where multipath isfound.

[0019]FIG. 7 depicts a multiple-input, multiple-output (MIMO) channelwith interference.

[0020]FIG. 8 depicts the use of an SOP in a single-input single-output(SISO) channel.

[0021]FIG. 9 depicts the use of an SOP in a MIMO channel according toone embodiment of the present invention.

[0022]FIG. 10 depicts the operation of an SOP in the context of oneembodiment of the present invention.

[0023]FIG. 11 depicts the application of spatial processing to aparticular SOP bin at the transmitter end according to one embodiment ofthe present invention.

[0024]FIG. 12 depicts the application of spatial processing to aparticular SOP bin at the receiver end according to one embodiment ofthe present invention.

[0025]FIG. 13 depicts the application of spatial processing to N SOPbins at the transmitter end according to one embodiment of the presentinvention.

[0026]FIG. 14 depicts the application of spatial processing to N SOPbins at the receiver end according to one embodiment of the presentinvention.

[0027]FIG. 15 depicts the use of a single spatial direction at thetransmitter end for each bin of an SOP according to one embodiment ofthe present invention.

[0028]FIG. 16 depicts the use of a single spatial direction at thereceiver end for each bin of an SOP according to one embodiment of thepresent invention.

[0029]FIG. 17 depicts the use of one or more common spatial weightingvectors for all SOP bins at the transmitter end according to oneembodiment of the present invention.

[0030]FIG. 18 depicts the use of one or more common spatial weightingvectors for all SOP bins at the receiver end according to one embodimentof the present invention.

[0031]FIG. 19 depicts the use of an encoder for each SOP bin accordingto one embodiment of the present invention.

[0032]FIG. 20 depicts the use of an encoder for each spatial directionaccording to one embodiment of the present invention.

[0033]FIG. 21 depicts the use of an encoder for each space/frequencysubchannel according to one embodiment of the present invention.

[0034]FIG. 22 depicts distribution of encoder output over allspace/frequency subchannels according to one embodiment of the presentinvention.

[0035]FIG. 23 depicts a detailed diagram of an encoder/interleaversystem according to one embodiment of the present invention.

[0036]FIG. 24 depicts a transmitter system wherein multiplespace/frequency subchannels are employed without spatialorthogonalization according to one embodiment of the present invention.

[0037]FIG. 25 depicts a receiver system wherein multiple space/frequencysubchannels are employed without spatial orthogonalization according toone embodiment of the present invention.

[0038]FIG. 26 depicts an exemplary technique for bit loading with atrellis coder that uses a one-dimensional QAM symbol constellation.

DESCRIPTION OF SPECIFIC EMBODIMENTS

[0039] Definitions

[0040] A “channel” refers to the input symbol to output symbolrelationship for a communication system. A “vector channel” refers to achannel with a single input and multiple outputs (SIMO), or multipleinputs and a single output (MISO). Each h_(j) entry in the vectorchannel h describes one of the complex path gains present in thechannel. A “matrix channel” refers to a channel with multiple inputs andmultiple outputs (MIMO). Each entry H_(i,j) in the matrix H describesthe complex path gain from input j to output i. A “space time channel”refers to the input to output relationship of a MIMO matrix channel, ora SIMO or MISO vector channel, that occurs when multipath signalpropagation is present so that the channel contains delay elements thatproduce inter-symbol interference (ISI) as explained below.

[0041] A “spatial direction” is a one dimensional subspace within amatrix or vector communication channel. Spatial directions need not beorthogonal. A spatial direction is typically characterized by a complexinput vector and a complex output vector used to weight transmitted orreceived signals as explained herein.

[0042] A “sub-channel” is a combination of a bin in a substantiallyorthogonalizing procedure (SOP) as explained below and a spatialdirection within that bin. A group of spatial subchannels within an SOPbin may or may not be orthogonal.

[0043] An “orthogonal dimension” is one member in a set of substantiallyorthogonal spatial directions.

[0044] A channel “subspace” is a characterization of the complex m-spacedirection occupied by one or more m-dimensional vectors. The subspacecharacterization can be based on the instantaneous or average behaviorof the vectors. A subspace is often characterized by a vector-subspaceof a covariance matrix. The covariance matrix is typically a time orfrequency averaged outer product of a matrix or vector quantity. Thecovariance matrix characterizes a collection of average channeldirections and the associated average strength for each direction.

[0045] A “two norm” metric for a vector is the sum of the squaredabsolute values for the elements of the vector.

[0046] A “Euclidean metric” is a two norm metric.

[0047] “Intersymbol interference” (ISI) refers to the self interferencethat occurs between the delayed and scaled versions of one time domainsymbol and subsequent symbols received at the output of a delay spreadcommunication channel. The channel delay spread is caused by thedifference in propagation delay between the various multipath componentscombined with the time domain response of the RF and digital filterelements.

[0048] A “substantially orthogonalizing procedure” (SOP) is a procedurethat plays a part in transforming a time domain sequence into a parallelset of substantially orthogonal bins, wherein the signals in one bin donot substantially interfere with the signals from other bins. Typically,the transformation from a time domain sequence to a set of substantiallyorthogonal bins requires a transmitter SOP with a set of input bins, anda receiver SOP with a set of output bins.

[0049] “Convolutional bit mapped QAM” (CBM-QAM) is the coding systemthat results when the output of a convolutional encoder are grouped andmapped to QAM constellation points.

[0050] Fading “structure” occurs when the fading behavior of one or moreentries in a channel matrix within an SOP bin is correlated across time,or frequency, or both. This structure can be exploited usingadvantageously designed estimation filters to improve channel estimationaccuracy given multiple frequency samples of the channel matrix entries,or multiple time samples, or both.

[0051] A “maximum likelihood sequence detector” is a sequence estimatorthat computes the most likely transmitted code sequence, from a set ofpossible sequences, by minimizing a maximum likelihood cost function.

[0052] An “antenna element” is a physical radiator used to transmit orreceive radio frequency signals. An antenna element does not involve anyelectronics processing components. A single radiator with twopolarization feeds is viewed as two antenna elements.

[0053] An “antenna array” is a collection of antenna elements.

[0054] A “burst” is a group of transmitted or received communicationsymbols.

[0055] Background Material

[0056] The disclosure herein assumes a background in digitalcommunication and linear algebra. The following references areincorporated herein by reference.

[0057] Wozencraft & Jacobs, Principles of Communication Engineering(1965).

[0058] Haykin, Adaptive Filter Theory, 2^(nd) Ed. (1991).

[0059] Strang, Linear Algebra, 3^(rd) Ed. (1988).

[0060] Jakes, Microwave Mobile Communication (1974).

[0061] Proakis, Digital Communications (1995).

[0062] Transmitter Overview

[0063]FIG. 1 depicts a transmitter system in accordance with oneembodiment of the present invention. Typically an information signalinput 2 includes a digital bit sequence, although other forms of digitaldata or analog data are possible. In the case of digital data, the inputdata sequence is first fed into an Encoder and Interleaving apparatus 10where the data is encoded into a symbol stream. The symbol stream istypically a sequence of complex digitized values that represent membersof a finite set. Each symbol can be a one dimensional value, or amultidimensional value. An exemplary one dimensional symbol set is a PAMconstellation. Note that in this discussion, it is understood that asymbol with in-phase and quadrature components, is considered to be acomplex one dimensional symbol, so that the QAM constellation is alsoviewed as a set of one dimensional symbols. An example multidimensionalsymbol set is a sequential grouping of QAM constellation members.

[0064] The purpose of the encoding process is to improve the bit errorrate of the transmitted signal by introducing some form of informationredundancy into the transmitted data stream. Useful encoding techniquescan involve combinations of a number of well known techniques such asconvolutional encoding with bit mapping to symbols, trellis encoding,block coding such as cyclic redundancy check or Reed Solomon coding withbit mapping or Automatic Repeat Queing. An interleaver is oftenadvantageous for distributing the transmitted information among thevarious subchannels available for transmission. This interleavingdistributes the effects of channel fading and interference so that longsequences of symbols with poor quality are not grouped closely togetherin the SOP bin sequence that is fed into the receiver decoder. In manyapplications, it is advantageous to perform a power and bit-loadingoptimization wherein the number of bits that are mapped to a givenencoder symbol, and the signal power assigned to that symbol, aredetermined based upon the measured communication quality of thespace-frequency information subchannel that carries the symbol stream.

[0065] After the digital data is encoded into a sequence of symbols, aTraining Symbol Injection block 20 may be used to place a set of knowntraining symbol values in the transmitter symbol stream. The purpose ofthe training symbols is to provide a known input within a portion of thetransmitted symbol stream so that a receiver may estimate thecommunication channel parameters. The channel estimate is used to aid indemodulation and decoding of the data sequence. The training symbols maybe injected periodically in time, periodically in frequency, or both. Itwill be obvious to one skilled in the art that blind adaptive spatialprocessing techniques can be utilized within each SOP bin at thereceiver as an alternative to training with known symbols. In such blinddetection implementations, Training Symbol Injection block 20 isunnecessary.

[0066] The data plus training symbol stream is then fed into aTransmitter Space-Frequency Pre-Processor (TSFP) block 30. The TSFPblock 30 performs two sets of advantageous processing steps on thesymbol stream before transmission. One processing step accomplishedwithin the TSFP is the transmitter portion of a substantiallyorthogonalizing procedure (SOP). When the transmitter portion of the SOPis combined with the receiver portion of the SOP, a set of parallel binsare created in such a manner that information transmitted within one bindoes not substantially interfere with information transmitted fromanother bin after the receive portion of the SOP is completed. Onepreferred SOP pair is the inverse fast Fourier transform (IFFT) at thetransmitter combined with the FFT at the receiver. Another advantageousSOP pair embodiment is a bank of multiple filter and frequency converterpairs (multi-band SOP) with one filter bank located at the transmitterand one filter bank located at the receiver as depicted in FIG. 2.Several other example SOPs including the Hilbert transform pair andgeneralized wavelet transform pairs will be obvious to one skilled inthe art. The other processing step accomplished in the TSFP is spatialprocessing. The spatial processing step typically multiplies one or moresymbols that are destined for transmission in a given SOP bin with oneor more spatial vector weights. For convenience in the followingdiscussion, the collection of spatial processing weights applied to thesignals transmitted or received in a given SOP bin are sometimesreferred to as a matrix. The spatial vector weights are optimized toobtain various desirable performance enhancements.

[0067]FIG. 2 depicts a digital baseband filter bank at the receiver anda filter bank located at the transmitter. Each filter of the transmitterfilter bank includes a mixer (frequency converter) 60, a bandpass filter70 and an interpolator 80. Each filter of the receiver filter bankincludes a bandpass filter 90, a mixer 60, and a decimator 100.

[0068] One transmitter embodiment optimizes the transmitter spatialvector weights so that the multiple subchannels in a given SOP bin canbe converted at the receiver into substantially independent receivedspatial subchannels wherein symbols from one subchannel do notsubstantially interfere with symbols from another subchannel. Anotherembodiment optimizes the transmitter spatial vector weight to improvethe received power of one or more spatial subchannels within each SOPbin, or to improve the average power of several spatial subchannelswithin several SOP bins. A further embodiment optimizes the transmitterspatial vector weights within each SOP bin to simultaneously increasethe power delivered to the desired receiver within one or more spatialsubchannels while reducing interference radiated to unintendedreceivers. A yet further embodiment spatial processes one or moresymbols within each SOP bin by multiplying each symbol with atransmitter weight vector that is fixed for all SOP bins, with theweight vectors optimized to increase the time or frequency average powerdelivered to one or more desired receiver spatial subchanels, andpossibly reduce the time or frequency averaged interference radiated tounintended receivers. This last embodiment is particularly useful in FDDsystems where multipath fading makes it impossible to estimate theforward channel from reverse channel data, but where the average forwardchannel subspaces are substantially similar to the average reversechannel subspaces. Another embodiment teaches simply routing each symbolfrom the encoder to one antenna element in each SOP bin without anyweighting. Other useful embodiments are discussed herein, and manyothers useful combinations of spatial processing with an SOP will becomeobvious to one skilled in the art. It is understood that one or moredigital filters are typically used in TSFP 30 to shape the transmittedRF signal spectrum.

[0069] Once the encoder symbol sequence is processed by TSFP 30, theprocessed symbol sequence includes a parallel set of digital time domainsignal sequences. Each of these time domain signal sequences is fed intoone input of a Modulation and RF System block 40. Modulation and RFSystem block 40 includes a set of independent RF upconverter chains thatfrequency convert the digital baseband signal sequence up to the RFcarrier frequency. This is accomplished using apparatus that includesdigital to analog converters, RF mixer apparatus, and frequencysynthesizer apparatus. The details of these elements of the inventionare well known and will not be discussed here.

[0070] The final step in the transmission process is to radiate thetransmitted signal using a Transmit Antenna Array 50. The antenna arrayscan be constructed from one or more co-polarized radiating elements orthere may be multiple polarizations. If there is multipath signalpropagation present in the radio link, or if there are multiplepolarizations in the antenna arrays, or if at least one of the antennaelements on one side of the link are in a disparate location from theother elements on the same side of the link, then the invention has theadvantageous ability to create more than one subchannel within each SOPbin. It is understood that one physical antenna reflector with a feedthat has two polarizations is considered as two antenna elements in allthat follows. There are no restrictions on the antenna array geometry orthe geometry of each radiating element. A transmitter system inventionmay adapt to provide optimized performance for any arbitrary antennaarray.

[0071] Receiver Overview

[0072]FIG. 3 depicts a receiver system according to one embodiment ofthe present invention. The RF signals from each of the elements of anAntenna Array 110 are downconverted to digital baseband using aDemodulation and RF System 120. Demodulation and RF System 120 includesthe RF signal processing apparatus to downconvert the RF carrier signalto a baseband IF where it is then digitized. After the digitizer, atiming and frequency synchronization apparatus is used to recover thetiming of the transmitted digital signal sequence. Several knowntechniques may be used for the purpose of synchronization and thesetechniques will not be discussed herein.

[0073] In certain embodiments of the invention, after Demodulation andRF System 120, the digital baseband signal is then fed into a Channel IDblock 130 and a Receiver Space-Frequency Processor (RSFP) block 140.Within Channel ID block 130, the characteristics of the digitalcommunication channel are estimated. The estimated channel valuesconsist of entries in a matrix for each SOP bin. The matrix containscomplex values representing the magnitude of the spatial channel withinthe SOP bin from one transmit antenna element to one receive antennaelement. The matrix channel estimate for each SOP bin is provided toRSFP block 140 and Decoder and Deinterleaving block 150.

[0074] Some embodiments of the invention involve improving channelestimation performance by exploiting the structured nature of thefrequency domain fading that exists in the matrix channels across SOPbins, exploiting the structure in time domain fading of the matrixchannels, or exploiting both the frequency and time domain fadingstructure that is present. By exploiting the frequency domain fadingcorrelation, the entire set of matrix channels within the SOP bins maybe estimated even when training information is transmitted in a subsetof the SOP bins. This allows for simultaneous transmission of trainingand data thus reducing overhead. By exploiting the time domaincorrelation of the channel fading within each SOP bin, channelestimation accuracy is increased for a given time epoch between trainingevents. This reduces the required frequency of training symboltransmission and thus further reduces training overhead. It isunderstood that it is also possible to separately exploit time domainand frequency domain correlation, with the most beneficial resultsoccurring if both correlation dimensions are used advantageously. It isto be understood that Channel ID block 130 is shown as a separatefunction even though it may share some elements with RSFP block 140 orDecoder and Deinterleaver block 150.

[0075] RSFP block 140 performs the receiver signal processing that isthe dual of the two sets of operations performed in TSFP 30. One of thesteps performed in RSFP 140 is the receiver half of the SOP. Asdiscussed above, the receiver half of the SOP completes thetransformation between the time domain channel with ISI to thesubstantially orthogonal set of bins. The second set of signalprocessing operations that can be performed in the RSFP is spatialprocessing. In one class of embodiments, the receiver spatial processingstep combines the output of the SOP bins using one or more vectorweighted inner product steps to form one or more one-dimensionalreceived spatial subchannels within each SOP bin. The receiver weightvectors are chosen to optimize an advantageous performance measure. Inone embodiment, wherein both the transmitter and receiver have knowledgeof the channel state information within each SOP bin, the transmitterspatial weight vectors and the receiver spatial weight vectors are bothchosen to optimize performance for a set of multiple substantiallyindependent subchannels within each SOP bin. As discussed above, thissignificantly increases the spectral efficiency of the system. Inanother embodiment wherein the transmitter does not have channel stateinformation, the receiver performs the spatial processing required tocreate multiple substantially independent subchannels within each SOPbin. In a further embodiment wherein the transmitter may or may not havechannel state information, the receiver reduces the effects ofinterference radiated from unintentional transmitters as well asperforming the spatial processing required to create multiplesubstantially independent subchannels within each SOP bin. A yet furtherembodiment optimizes the receiver spatial vector weights within each SOPbin to simultaneously increase the received power and reduce thedetrimental effects of interference received from unintentionaltransmitters. An additional embodiment involves forming one or morevector weights, that are fixed for all SOP bins, where the vectorweights are optimized to simultaneously increase the time or frequencyaveraged received power for one or more spatial subchannels, whilepossibly also reducing the time or frequency averaged interference powerreceived from unintended transmitters.

[0076] As discussed herein, certain embodiments involve simply passingthe vector samples received in each SOP bin to Decoder andDeinterleaving block 150 without performing any spatial processing. Itwill be obvious to one skilled in the art that other combinations oftransmitter spatial weight vector optimization techniques and receiverspatial weight vector optimization techniques can be constructed aroundthe principle concept of spatial processing in combination with an SOP.Other embodiments are discussed herein. One experienced in the art willbe able to recognize additional embodiments that involve advantageouscombination of an SOP with spatial processing at the receiver or thetransmitter. It is understood that one or more digital filters aretypically used in RSFP block 1400 to shape the received RF signalspectrum.

[0077] The outputs of RSFP block 140 are fed into Decoder andDeinterleaving (DD) block 150. There are two broad exemplary classes ofoperation for the DD block 150. In the first exemplary broad class ofembodiments, DD block 150 decodes a symbol sequence which was encodedand transmitted through a multitude of SOP bins with one or moresubstantially independent subchannels. The decoder includes theappropriate receiver counterparts for the combination of encodersselected for the transmitter. A preferred embodiment includes adeinterleaver, a trellis decoder or convolutional bit mapping decoderemploying a scalar weighted Euclidean maximum likelihood sequencedetector, followed by a Reed Solomon decoder, followed by an ARQ systemto correct Reed Solomon codeword errors. In the second exemplary broadclass of embodiments, DD block 150 decodes a sequence ofmultidimensional symbols, or groups of adjacent one dimensional symbols,with each multidimensional symbol or group of one dimensional symbolsbeing received in an SOP bin. Typically, the symbol sequences aretransmitted without weighting or with weighting that optimizes somemeasure of average signal quality.

[0078] In an alternative embodiment, trellis encoded symbols are groupedand interleaved in a manner such that the symbols transmitted from theantenna elements within a given SOP bin form a vector that is drawn fromeither a multidimensional QAM encoder output symbol, or a sequence ofone dimensional QAM encoder output symbols that have adjacent locationsin the pre-interleaved encoder output sequence. In this way, a maximumlikelihood vector decoder may be constructed given an estimate of thechannel matrix that is present within each SOP bin. The maximumlikelihood decoder computes the weighted vector Euclidean metric giventhe deinterleaved received vector from each SOP bin, the deinterleavedmatrix channel estimates from each SOP bin, and the transmitted vectorsymbol trellis state table.

[0079] In another alternative embodiment, either of the aforementionedencoder embodiments will have preferable performance if the encoderpolynomial and symbol constellation set are optimized to improve the biterror rate performance given the characteristics of the matrix channelfading that occurs in each SOP bin. One particular metric that is wellsuited for a code polynomial optimization search is the product of thetwo norms of the vector difference between the correct transmittersymbol vector and the error symbol vector.

[0080] The output of DD block 150 is the estimated bit stream at thereceive end of the radio link.

[0081] It is to be understood that all transmitter embodiments of thepresent invention may be adapted for use with a receiver accessing thechannel through a single channel output such as a single receiverantenna element. Furthermore, all receiver embodiments of the presentinvention may be adapted for use with a transmitter accessing thechannel through a single channel input such as a single transmitterantenna element. It is understood that the channel is then a vectorchannel. Such multiple-input single-output (MISO) and single-inputmultiple output (SIMO) systems are within the scope of the presentinvention.

[0082] Space-Frequency Communication in a Multipath Channel

[0083] Before developing the signal processing of the present invention,a physical description and mathematical description of wireless channelsare provided. Many wireless communication channels are characterized bymulti-path, where each path has associated fading and propagation delay.Multipath may be created by reflections in the physical radio path,multiple antenna polarizations, antenna elements located in disparatelocations, or a combination of any of these. One scenario in whichmultipath is created is illustrated in FIG. 4. A Base 152 transmitsinformation to and receives information from a remote unit 170A or 170B.Base 152 possesses one or more antenna elements referred to as an array55. Similarly, the Remote Units possess their own arrays 55. Atransmitted signal propagates along multiple paths 155A-C created byreflection and scattering from physical objects in the terrain 160A-D.

[0084] Multipath signal propagation such as that depicted in FIGS. 4-6can give rise to spatially selective fading, delay spread, frequencyfading, and time fading. Spatial fading occurs as the various wavefrontsarriving at the receiver from different propagation paths combine withconstructive and destructive interference at different points in space.An antenna array located within this spatially selective field willsample the field at various locations so that the signal strength ateach array element is different. Delay spread occurs due to thediffering propagation path lengths. The channel delay spread gives riseto a frequency selective digital communication channel at each antennaelement. This frequency response is different for each antenna elementby virtue of the frequency dependent spatial fading. Finally, if eitherthe transmitter, or the receiver, or objects in the terrain are moving,the frequency selective spatial fading will vary as a function of time.The present invention is unique in that it is capable of efficiently andeconomically adapting to the time varying space-frequency channelresponse to make advantageous use of the inherent properties of suchchannels.

[0085] For several decades, the primary focus of the prior art has beento somehow mitigate the effects of the multipath channel. Thisconventional approach is ill-advised since multipath channels give riseto a multiplicative capacity effect by virtue of the fact that themultipath induces a rank greater than one in the matrix channel presentin each SOP bin. This provides opportunity to form multiple parallelsubchannels for communication within each SOP bin. Thus, one shouldutilize multipath to improve communication performance rather thanattempt to mitigate its effects. A substantial advantage provided by thepresent invention is the ability to efficiently and economically exploitthe inherent capacity advantages of multipath channels using acombination of an SOP and spatial processing or spatial coding. No otherstructures are known to efficiently exploit this fundamental advantagein the presence of substantially frequency selective multipath channels.

[0086]FIG. 5 illustrates another wireless channel scenario in whichmultipath is present. A Base 152 with an antenna array 55 transmitsinformation to and receives information from a Remote 170C with anantenna array 55. In this case, both Base and Remote antenna arrays 55both have elements with differing polarizations. Thus multipath signalpropagation exists even if there are no significant reflections in thephysical environment. The direct line of sight paths 155B, 155E eachcorresponding to one of the polarizations in the array elements, aresufficient to create a matrix channel with a rank greater than onewithin each SOP bin, even if the other reflected radio paths 155A, 155C,155D, and 155F are insignificant or nonexistent.

[0087] It is known that such line of sight polarization (reflectionfree) channels can be decomposed into two parallel communicationchannels by using high performance dual polarization antennas, one ateach end of the radio link, in combination with high performancereceiver and transmitter electronics apparatus. In this prior art, thequality of the parallel communication channels is limited by the degreeto which the two polarization channels remain independent. In general,maintaining the manufacturing tolerances and installation alignmentprecision in the antennas and electronics required to achievesubstantially orthogonal spatial subchannels at the output of thephysical receive antenna is relatively expensive. Slight manufacturingerrors and component variations can lead to a significant cross-talkinterference between the multiple polarizations present in the radiochannel. In contrast, an advantageous feature of the invention is thatthe different polarizations present in the wireless channel may have anarbitrary degree of cross-talk interference, and the cross-talkinterference may be frequency dependent without loss of performance. Insuch cases, the invention provides an economical and efficient methodfor fully exploiting the multi-dimensional nature of the multiplepolarization channel. It is understood that the invention can providefurther capacity advantage if the multiple polarization channel also hasreflected signal paths. This additional multipath results in anadditional increase in the channel matrix rank in each SOP bin that canbe further exploited to improve the capacity of the channel.

[0088]FIG. 6 depicts another wireless communication scenario in whichmultipath is present and can be exploited to create multiple dimensionsfor communication. In FIG. 6, two Bases 152A and 152B with antennaarrays 55 communicate with Remote Units 170A and 170B that also possessantenna arrays 55. In this case, the composite channel is defined as theMIMO channel between the antennas of the two Bases 152A and 152B and theantennas of the Remote Units 170A and 170B. Note that this channelincludes direct line of sight paths 155B and 153B as well as thereflected paths 155A, 155C, 153A, 153C, and 153D. By virtue of thespatial separation between two Bases 152A and 152B, even if thereflected paths are insignificant or nonexistent, this channel containsmultipath that can be exploited using the invention. In addition, thechannel from the antennas of the two Bases to the antennas of one Remoteis again a matrix channel, with rank greater than one, within each SOPbin so that multiple parallel dimensions for transmission may becreated. In these types of applications, the present invention providesfor the ability to reduce interference radiate to unintentionalreceivers. Furthermore, the present invention provides the capability ofreducing the detrimental effects of received interference fromunintentional transmitters.

[0089] Thus it can be seen that multiple transmitter antenna elements ormultiple antenna elements may be either co-located or be found atdisparate locations. The following symbol channel model applies to allof the above multipath radio propagation cases illustrated by FIGS. 4-6.The channel impulse response includes the effects of the propagationenvironment, as well as the digital pulse shaping filters used in TSFP30 and RSFP 140, the analog filters used in Modulation & RF System 40and Demodulation & RF System 120. Due to the difference in propagationdelay between the various multipath components combined with the timedomain response of the RF and digital filter elements, a single symboltransmitted into the channel is received as a collection of delayedcopies. Thus, delayed and scaled versions of one symbol interfere withother symbols. This self interference effect is termed intersymbolinterference or ISI. The delay spread parameter, denoted by ν, is theduration in symbol periods of the significant portion of the channelimpulse response.

[0090] As the transmitted symbol rate is increased or as the physicalgeometries in the channel become larger, the delay spread can become solarge that conventional space-time processing systems become highlycomplex. An advantage of the present invention is that the signalprocessing complexity is relatively low even when the delay spreadbecomes extremely large. This allows for the economical application ofMIMO space-frequency processing techniques at high digital data rates.This efficient use of signal processing comes about because theinvention allows the space-time channel to be treated as a set ofsubstantially independent spatial subchannels without sacrificingchannel capacity. In contrast, conventional approaches either attempt toequalize the much more complex space-time channel or alternativelysacrifice capacity.

[0091] The channel is modeled as time-invariant over the time spanned bya burst of N data symbols, but varying from one burst to another. Thisblock time invariant assumption produces a channel model that issufficiently accurate for channels wherein the block duration is shortcompared to the channel fading, or (N+2ν)T<<Δ_(β), where Δ_(β) is thecorrelation interval¹. Other models are available wherein the channelvaries continuously, but these models add unnecessary complication tothe present discussion. It is understood that rapid time variation inthe channel can be another motivation for choosing one of the other SOPalternatives in the presence of fading rates that are rapid with respectto the burst frequency. One skilled in the art will be aware of thepertinent issues for a given application. For example, OrthogonalFrequency Domain Multiplexing (OFDM) is an SOP composed of an IFFT andcyclic prefix as the transmitter SOP, and an FFT as the receiver SOP.With OFDM, one pertinent issue is frequency domain inter-carrierinterference (ICI), which can occur in OFDM systems with extremely rapidfading. Such pertinent issues shape the appropriate choice of channelmodels for various SOP basis functions.

[0092] With this background discussion, it can be verified by oneskilled in the art that the relationship between the transmitted burstof baseband symbols and the received burst of baseband samples may beadequately expressed as the space-time equation,

x(k)=G(k)z(k)+I(k),

[0093] where the index k represents bursts. The composite channel outputfor one burst of data, x(k), is written with all time samples appear insequence for every receive antenna 1 to M_(R),

x(k)=└x ₁(1) . . . x ₁(N+ν−1) . . . x _(M) _(R) (1) . . . x _(M) _(R)(N+ν−1)┘^(T).

[0094] Likewise, the input symbol vector is written,

z(k)=└z ₁(1) . . . z ₁(N) . . . z _(M) _(T) (1) . . . z _(M) _(T)(N)┘^(T)

[0095]¹The correlation interval here is defined as the time periodrequired for the fading parameter time-autocorrelation function todecrease to some fraction of the zero-shift value.

[0096] The quantity I(k), defined the same as x(k) and z(k), representsboth noise and interference. The MIMO channel matrix, G(k), is composedof single-input single-output (SISO) sub-blocks, $\begin{matrix}{{G(k)} = {\begin{bmatrix}{G_{1,1}(k)} & \cdots & {G_{1,M_{T}}(k)} \\\vdots & ⋰ & \vdots \\{G_{M_{R},1}(k)} & \cdots & {G_{M_{R},M_{T}}(k)}\end{bmatrix} \in {C^{{NM}_{T} \times {({N + v})}M_{R}}.}}} & (1)\end{matrix}$

[0097] Furthermore, each of the SISO sub-blocks, G_(i,j)(k) , is aToeplitz matrix describing the input-output relationship between thetransmitted symbol burst and the received symbol burst for antenna pair(i,j). This MIMO space-time channel is illustrated by FIG. 7, whichshows SISO sub-blocks 180A-D and the addition of interference for eachreceiver sample.

[0098] Space-Frequency Processing

[0099] Embodiments of the present invention uses space-frequencyprocessing at either the transmitter or receiver, or both, to createeffective communication systems in wireless channels. Generally, theprocessing substantially eliminates the ISI caused by the channelcorrelation across space (antenna correlation) and time (delay spread).This processing greatly simplifies the design of the remaining functionsthat comprise a complete communication system, including coding andmodulation. Furthermore, the processing approach is based upon acapacity-achieving structure for the MIMO wireless communicationchannel. Space-frequency processing is composed of one or more of thefollowing: an SOP, a transmit spatial processor, and a receive spatialprocessor.

[0100] Substantially Orthogonalizing Procedure

[0101] The use of an SOP in a SISO channel is considered first in orderto illustrate the invention's ability to eliminate ISI across space andtime. The SOP is composed of signal processing operations implemented atboth the transmit and receive sides of the channel. This is illustratedin FIG. 8 where a Transmitter SOP processor 190 and a Receiver SOPprocessor 200 jointly perform a complete SOP. The SOP ensures that the Ninput symbols, in bin 1 through bin N, are transmitted through thechannel in such a way that each output symbol is substantiallyinfluenced by only the input symbol of the same frequency bin. Forexample, the input symbol in bin 1 is the only symbol to havesubstantial influence on the output symbol value in bin 1.

[0102] This concept generalizes to the MIMO system as shown in FIG. 9.For the MIMO system, each transmitter antenna 51 is preceded by one ofM_(T) identical Transmitter SOP processors. Likewise, each receiverantenna 111 precedes one of M_(R) identical Receiver SOP processors.Hence, the processing path for any transmitter-receiver antenna paircontains a jointly performed complete SOP. In other words, there existM_(R)M_(T) SISO SOPs in the MIMO system. By exploiting the property ofsuperposition, this collection of SISO SOPs comprise a MIMO SOP whereany two symbols communicated in different bins exhibit substantiallyreduced crosstalk, irrelevant of the antennas by which the symbols weretransmitted and received. Therefore, the SOP establishes N substantiallyindependent MIMO spatial channels.

[0103] Many different SOP implementations exist, including an IFFT-FFTpair, a bank of multiple narrow-band filters, and generalized wavelettransform pairs. One advantageous example of an SOP is the use of afrequency transform combined with a burst cyclic prefix applicationprocedure processor 207, as shown in FIG. 10. There is also a cyclicprefix removal procedure processor 206 at the receive end. When thefrequency transform is an IFFT-FFT pair 205 and 208 as shown in FIG. 10,this particular SOP is commonly referred to as discrete orthogonalfrequency division multiplexing (OFDM). Hence, this embodiment of theinvention combines the OFDM SOP with multiple input antennas, ormultiple output antennas, or both multiple input and multiple outputantennas. The present embodiment is thus termed matrix-OFDM (MOFDM).

[0104] The analysis presented for MOFDM will have a substantiallysimilar form as other choices for the SOP. These alternative embodimentshave certain advantages and drawbacks as compared to the OFDM SOP. Forexample, the multi-band SOP does not completely eliminate ISI, but it ismore robust to certain types of narrow-band interfering signals becausethe interference can be more confined within a given SOP bin as comparedto the OFDM SOP. The ISI that can be present in the multi-band SOP couldmake it advantageous to use pre-equalization or post-equalizationstructures in conjunction with the spatial processing within a given SOPbin. While this complicates the spatial processing, the complexitydrawback may be outweighed by other requirements such as robustness tointerference or the need to separate the SOP bins by relatively largefrequency separation. Only the OFDM SOP will be analyzed in detailherein and it will be understood that one may exploit the other SOPchoices as needs dictate.

[0105] As depicted in FIG. 10, the exemplary SOP operates in thefollowing fashion. The symbols from the transmit spatial pre-processor,z_(j)(n), considered to be in the frequency domain, are organized intoM_(T) vectors of N complex symbols. Each of these vectors is thenconverted to the time-domain using an N-pointinverse-fast-Fourier-transform (IFFT) procedure 205. Each of theparallel M_(T) time-domain sequences has a cyclic prefix added to thebeginning, so that the last ν elements in the IFFT output sequence forma pre-amble to the N-element IFFT output. The cyclic prefix operation isgiven by:

[z(1) . . . z(N)]^(T)

[z(N−ν+1) . . . z(N)z(1) . . . z(N)]^(T)

[0106] The application of the cyclic prefix is performed by cyclicprefix application procedure processor 207. For each antenna, the(N+ν)length sequences are passed to the RF transmit chain for D/Aconversion and modulation.

[0107] Likewise, each RF receiver chain produces a sampled sequence oflength N+ν. Cyclic prefix removal procedure processors 206 remove thecyclic prefix from each sequence by discarding the first ν data symbols,resulting in M_(R) vectors of N complex symbols. Each of these M_(R)sequences is then processed with an N-point fast-Fourier-transform(FFT). These symbols are then passed to the receiver spatial processor.

[0108] The effect of the SOP is to substantially remove the ISI betweenany two symbols assigned to different bins, for any pair of transmit andreceive antennas. Therefore, for each IFFT-FFT bin n, the receivedsignal values for each antenna, x(n), are related to the transmittedfrequency-domain symbols, z(n), through the expression,

x(n)=H(n)z(n)+I(n)∀n  (10)

[0109] where x(n) is a complex M_(R)-element vector at SOP bin n, z(n)is a complex M_(T)-element symbol vector at bin n, and I(n) is theinterference and noise at all receive antennas for bin n. Note that atime index is not included in the above equation since it is assumedthat channel is time-invariant over the length of a burst. The spatialsub-channels, H(n), are M_(R) by M_(T) element matrices that describethe spatial correlation remaining in the wireless channel after the SOP.For the MIMO case, each SOP bin may be characterized by a matrix ofcomplex values, with each value representing the path gain from a giventransmit antenna element to a given receive antenna element in thatparticular SOP bin.

[0110] To understand the result given by Equation(10), it is instructiveto show how the SOP pre-processor and post-processor acts upon thetime-domain channel. The MIMO time-domain channel, G(k), containsM_(R)M_(T) Toeplitz matrices that describe the time-domain input-outputbehavior of each antenna pair (see eq. 1). This channel formulation isdepicted in FIG. 10. It is well known that by adding a cyclic prefix atthe transmitter and subsequently removing the prefix at the receiver, aToeplitz intput-output matrix is transformed into a circulantinput-output matrix (the jth row is equal to the jth row cycliclyshifted by i-j elements). Therefore, the each G_(i,j) in FIG. 10 istransformed into a circulant {tilde over (G)}_(i,j). The MIMO circulantmatrices are delimited in FIG. 10 by {tilde over (G)}.

[0111] This particular class of SOP exploits the fact that any circulantmatrix can be diagonalized by a predetermined matrix operator. One suchoperator is a matrix of the FFT basis vectors. That is, for anycirculant matrix {tilde over (G)},

D=Y{tilde over (G)}Y^(H)

[0112] where D is some diagonal matrix and the scalar elements of Y are,$y_{mn} = {\frac{1}{\sqrt{N}}{^{{- j}\quad 2\quad \pi \quad m\quad {n/N}}.}}$

[0113] Applying M_(T) IFFT operations at the transmitter and M_(R) FFToperations at the receiver is described mathematically by apre-multiplication of a NM_(R)×NM_(R) block diagonal FFT matrix andpost-multiplication of a NM_(T)×NM_(T) IFFT matrix. For example, theformer matrix is defined, $Y_{(M_{R})} = {\begin{bmatrix}Y & \quad & 0 \\\quad & ⋰ & \quad \\0 & \quad & Y\end{bmatrix}.}$

[0114] Therefore, including the transmitter IFFT and receiver FFToperations, the input-output relationship is described by${{Y_{(M_{R})}\overset{\sim}{G}Y_{M_{T}}^{H}} = \begin{bmatrix}D_{1,1} & \cdots & D_{1,M_{T}} \\\vdots & ⋰ & \vdots \\D_{M_{R},1} & \cdots & D_{M_{R},M_{T}}\end{bmatrix}},$

[0115] where D_(i,j) is the diagonal matrix containing the SOP binstrengths for the antenna pair (i,j). Pre-multiplication andpost-multiplication by permutation matrices P_(T) and P_(R) representsthe collection of all antenna combinations that correspond to a commonfrequency or SOP bin.

[0116] This collection process, depicted in FIG. 10, results in a blockdiagonal matrix that relates the intputs and outputs:${{P_{R}Y_{(M_{R})}\overset{\sim}{G}Y_{M_{T}}^{H}P_{T}} = \begin{bmatrix}{H(1)} & \quad & 0 \\\quad & ⋰ & \quad \\0 & \quad & {H(N)}\end{bmatrix}},$

[0117] which is equivalent to Equation (10).

[0118] Spatial Processing

[0119] The spatial processing procedure is now considered. Since the SOPestablishes N MIMO spatial channels that are substantially independentfrom one another (Equation 10), one can consider the spatial processingwithin each bin separately. Representative application of spatialprocessing to frequency bin 1 will be considered as shown in FIG. 11 atthe transmitter and FIG. 12 at the receiver. FIG. 11 shows M symbols:z(1,1) through z(1,M). The notation z(n,m) refers to the symboltransmitted in bin n and spatial direction m. These M symbols willjointly occupy frequency bin 1. Each TSW 210A-C applies aweight vectorto the symbol appearing at its input, and the elements of the resultantvector are routed to M_(T) summing junctions 211. One may consider theTSWs as being multipliers taking each input symbol and multiplying it bya vector that corresponds to a spatial direction in M_(T)-space.Furthermore, the M vectors define a subspace in M_(T)-space. Note thatthe TSW vectors are considered to be column vectors in the discussionthat follows. When these M vectors are collected into a matrix, theresult is an input orthogonalizing matrix or beneficial weighting matrixfor that bin. For each input bin, a vector including symbols allocatedto subchannels corresponding to the bin is multiplied by the inputorthogonalizing matrix to obtain a result vector, elements of the resultvector corresponding to the various transmitter antenna elements.Together, the TSWs 210A-C make up one embodiment of a Transmit SpatialProcessor (TSP) 230.

[0120] Each RSW 220A-C accepts M_(R) inputs, one from each receiverantenna path. Within the m^(th) RSW, a weight vector is applied to theinputs (i.e. an inner-product is performed) thereby producing a receivedsignal sample x(1,m):${{x\left( {1,m} \right)} = {{u\left( {1,m} \right)}\begin{bmatrix}{x_{1}(1)} \\\vdots \\{x_{M_{R}}(1)}\end{bmatrix}}},$

[0121] where u(1,m) is the RSW for bin 1 and spatial direction m.Similar to a TSW, a RSW vector has an associated direction inM_(R)-space. Each RSW may also be considered to be a multiplier. Thisvector is considered to be a row vector. When these M RSW vectors arecollected into a matrix, the result is an output orthogonalizing matrixor beneficial weighting matrix for that bin. When a vector includingsymbols in a particular output bin produced by the SOP for each receiverantenna is multiplied by the output orthogonalizing matrix, the resultis a vector including symbols received in that bin for various spatialdirections. Together, the RSWs 220A-220C represent one embodiment of aReceive Spatial Processor (RSP) 240.

[0122] Through proper choice of the weight vectors applied via the TSWsand RSWs, the M spatial directions can be made substantially orthogonalto one another. The result is that the received signal sample x(1,m)depends only upon input symbols z(1m) and not the M-1 other inputsymbols for SOP bin 1. Methods for selecting the TSP and RSP weightvectors are described in detail below.

[0123] The spatial processing described above can be applied to theother N−1 frequency bins in addition to frequency bin 1. The blockdiagram for such a system is depicted in FIG. 13 for the transmitter andFIG. 14 for the receiver. SOP processors 190 and 200 ensure that thefrequency bins remain substantially orthogonal to one another while TSP230 and RSP 240 ensure that M substantially orthogonal spatial channelsexist within each frequency bin. The net result is that NM substantiallyparallel subchannels are constructed within the MIMO communicationsystem. In other words, the combination of SOP processors 190 and 200,TSP 230, and RSP 240 create a set of substantially independentspace-frequency subchannels,

x(n,m)=H(n,m)z(n,m)+I(n,m)∀n,m.

[0124] This simultaneous substantial orthogonalization of space andfrequency can result in a significant increase in spectral efficiencysince multiple data streams are being communicated through the channel.Note that the number of substantially independent subchannels possible,in the multipath case, is equal to the number of SOP bins multiplied bythe number of transmit antennas or the number of receive antennas,whichever is smaller. Therefore, the total number of space-frequencysubchannels is less than or equal to N min(M_(T),M_(R)), when multipathis present.

[0125] An exemplary set of TSWs and RSWs are derived from the singularvalue decomposition (SVD) of the spatial channel matrix for each bin,

H(n)=U(n)Σ(n)V(n)^(H).

[0126] The input singular matrix, V(n), contains M_(T) column vectorsthat define up to M_(T) TSWs for bin n. Likewise, the output singularmatrix, U(n), contain M_(R) column vectors that when Hermitiantransposed, define up to M_(R) RSW row vectors for bin n. The TSWs andRSWs for other bins are determined in the same fashion, through an SVDdecomposition of the spatial matrix for that bin. Using this spatialprocessing, substantially independent multiple streams of symbols can betransmitted and received. The strength of each subchannel is equal toone of the elements of the diagonal matrix Σ. These subchannelsstrengths will vary. Therefore, the subchannels will have varying signalto noise ratios and information capacity. For this reason, it may bepreferable to transmit and receive only on a subset of the possiblesubchannels, or M<min{M_(T),M_(R)}. For example, it may be improvidentto use processing complexity on the weakest subchannels that may have avery small information carrying capacity. In this case, spatialprocessing is used to increase the received power of one or moreparallel symbol streams. It may also be preferable to use codingtechniques to leverage strong subchannels to assist in the use of weakersubchannels. It may also be preferable to allocate either bits ortransmit power among the subchannels to maximize the amount ofinformation communicated.

[0127] The exemplary spatial processing described above requirescooperation between the transmitter and receiver to effectivelyorthogonalize the spatial channel for each bin. Alternatively, thisorthogonalization can be accomplished at only one end of the link. Thiscan be advantageous when one end of the link can afford morecomputational complexity than the other end. In addition, spatialorthogonalizing at one end can be advantageous when the channel model isknown only at that end.

[0128] Consider the case where the orthogonalization is done at thereceiver. Symbols are transmitted along directions defined by some setof TSWs, v(n,m). When M TSWs corresponding to the same bin are collectedinto a matrix V(n), the composite spatial channel is,

H′(n)=H(n)V(n).

[0129] This composite channel describes the MIMO channel in bin n fromthe M-inputs to M_(R) outputs. The spatial processing at the receivercan substantially orthogonalize this composite channel, H′(n), byapplying appropriate RSWs even if the transmitter does no spatialprocessing. Let these RSWs be defined as the row vectors of theweighting matrix, W_(R)(n).

[0130] Two exemplary methods for determining W_(R)(n) are referred to asthe zero-forcing (ZF) solution and minimum-mean-square-error (MMSE)solution. In the ZF approach, the weighting matrix is thepseduo-(left)-inverse of the composite channel,

W _(R)(n)=H′(n)^(⊥).

[0131] This results in,

W _(R)(n)H′(n)=I,

[0132] where the identity matrix is M by M. Hence, the ZF solution, notonly orthogonalizes the spatial channel for bin n, but it equalizes thestrengths of each resulting subchannel. However, the signal-to-noiseratio for the various subchannels can vary widely. One skilled in theart will recognize that the ZF solution can result in amplification ofthe interference and noise unless the composite channel, H′(n), isnearly orthogonal to begin with.

[0133] An MMSE solution, on the other hand, does not amplify noise. Forthe MMSE approach, the weight, W_(R)(n), satisfies,${\min\limits_{W_{R}{(n)}}{E\left\{ {{{{W_{R}(n)}{x(n)}} - {z(n)}}}^{2} \right\}}},$

[0134] or,

W _(R)(n)=R _(z(n)x(n)) R _(x(n)),⁻¹

[0135] where R_(x(n)) is the covariance matrix for x(n) and R_(z(n)x(n))is the cross-covariance between z(n) and x(n). Using,

x(n)=H′(n)z(n)+I′(n),

[0136] and the fact that R_(z(n))=σ_(z) ²I, results in the MMSE weight,${W_{R}(n)} = {{H^{\prime}(n)}^{H}{\left( {{{H^{\prime}(n)}{H^{\prime}(n)}^{H}} + {\frac{1}{\sigma_{z}^{2}}R_{I^{\prime}}}} \right)^{- 1}.}}$

[0137] Note that when I(n) is spatially white noise, then R_(I)=σ_(z)²I.

[0138] Similarly to the above orthogonalization at the receiver, thechannel can be orthogonalized at the transmit end only. For this tooccur, the transmitter is required to have knowledge of the RSWs to beused by the receiver. In a TDD channel, where the channel exhibitsreciprocity, these RSWs can be learned when that transceiver uses TSWdirections equal to the RSW directions. Alternatively, the receiver maynot do any spatial processing, so the transmitter is responsible forspatial orthogonalization.

[0139] In this case, the composite channel is

H′(n)=U(n)H(n),

[0140] where the matrix U(n) is composed of the RSW row vectors, u(n,m).This composite channel describes the MIMO channel in bin n from M_(T)inputs to M outputs. Similar to the previous case, the transmitter cansubstantially orthogonalize this composite channel, H′(n), by applyingappropriate TSWs. These TSWs are the column vectors of the weightingmatrix, W_(T)(n).

[0141] The transmit weighting can be determined using the ZF or the MMSEapproach. In the ZF approach, the weighting matrix is equal to thepseudo-(right)-inverse of H′(n). The MMSE solution satisfies${\min\limits_{W_{T}{(n)}}{E\left\{ {{{{H^{\prime}(n)}{W_{T}(n)}{z(n)}} + {I^{\prime}(n)} - {z(n)}}}^{2} \right\}}},$

[0142] An important simplification to the general space-frequencyprocessing technique is the use of only one spatial direction for eachbin of the SOP. This case is depicted in FIG. 15 for the transmitter andFIG. 16 for the receiver. In this case, only N subchannels are created.The N input symbols, z(1,1) through z(N,1), are processed by N TSWs210A-B that weight and allocate these N symbols among the M_(T)identical SOP processors 190. At the receiver, the antenna samples areprocessed by M_(R) SOP processors 200. The M_(R) SOP outputscorresponding to a common bin are weighted and combined in N RSWs220A-B. With N such weightings, the result is N outputs, x(1,1) throughx(N,1), of the N substantially orthogonal subchannels.

[0143] When only one spatial direction is used in the TSP and RSP, oneexemplary choice for the particular weightings are the TSW and RSWdirections that result in maximum subchannel strength. This maximizesthe signal-to-noise ratio (SNR) of the received signals, x(1,1) throughx(N,1). In this case, the optimal weightings should satisfy,${\max\limits_{{u{(n)}},{v{(n)}}}{{{u(n)}{H(n)}{v(n)}}}^{2}},$

[0144] with the implicit constraint on the size (2-norm) of both the RSWweight u(n) and the TSW weight v(n). To determine the solution to thisoptimization problem, consider the SOP outputs for bin n when a singleTSW, v(n,1), is used, $\begin{bmatrix}{x_{1}(n)} \\\vdots \\{x_{M_{R}}(n)}\end{bmatrix} = {{{H(n)}{v\left( {n,1} \right)}{z\left( {n,1} \right)}} = {{h(n)}{{z\left( {n,1} \right)}.}}}$

[0145] The quantity h(n) is referred to as the received channel vector.A channel identification technique is used to determine the receivedchannel vector. Therefore, the optimal RSW weight is equal to theHermitian of the received channel vector, h(n),

u(n)=h(n)^(H).

[0146] Note that this is true regardless of the particular value ofv(n). The optimal TSW direction, on the other hand, satisfies,${{\max\limits_{v{(n)}}{{u(n)}{H(n)}{v(n)}}} = {\max\limits_{v{(n)}}{{v(n)}^{H}{H(n)}^{H}{H(n)}{v(n)}}}},$

[0147] where the optimal RSW direction has been used. The optimal TSWfor bin n is equal to the scaled maximum eigenvector of the matrixH(n)^(H) H(n). One skilled in the art will recognize that the optimalRSW is also equal to the scaled maximum eigenvector of H(n)H(n)^(H).

[0148] A further advantageous simplification of the above techniques isthe use of one or more common TSW and RSW directions for all bins. Inother words, every bin has the same TSW and RSW weights. These weightvectors may also consider delay elements. In one embodiment, theseweights are determined to maximize the SNR of the received signals,averaged over frequency n. This is depicted in FIG. 17 for thetransmitter and FIG. 18 for the receiver. Consider this embodiment withone spatial direction. In this case, the TSW and RSW weights satisfy,$\begin{matrix}{{\max\limits_{u,v}{E_{n}\left\lbrack {u\quad {H(n)}v} \right\rbrack}^{2}},} & 50\end{matrix}$

[0149] Note that the expectation operator, E_(n), represents averagingover SOP bins. This averaging could also be done over multiple bursts inaddition to frequency. The solution to this problem is when v is equalto the maximum eigenvector of

R _(d) =E _(n) {H ^(h)(n)H(n)},  51

[0150] and u is equal to the maximum eigenvector of the covariancematrix formed from averaging the outer product of the receive vectorchannel,

R _(h) =E _(n) {h(n)h(n)^(H)},  52

[0151] The quantity R_(d) is the spatial covariance matrix thatdescribes preferable directions to transmit to the desired receiver, adesired subspace.

[0152] This technique can be generalized to the case where multipledirections are utilized. In this case, M TSWs and M RSWs are determinedto maximize the average (over bin) SNR received through the M spatialdirections. The M spatial directions will not necessarily be orthogonalto each other. Therefore, there will be spatial crosstalk in thereceived symbols. Multidimensional encoding and decoding techniquesdiscussed below can then achieve a multiplicative rate increase in thepresence of such crosstalk.

[0153] Alternatively, the receiver can spatially orthogonalize thesubchannels by further weighting of the M outputs from the RSWs. Thecomposite spatial channel at bin n, with the RSWs and TSWs included is

H′(n)=UH(n)V,  53

[0154] where the matrix U is made up rows equal to the RSW directionsand V is a matrix with columns equal to the TSW directions. Since U andV were determined based on an average SNR criterion for all bins, thecomposite matrix H′(n) will not be diagonal. Hence, the receiver canapply the additional weight, W_(R)(n), to orthogonalize H′(n).Alternatively, the transmitter can use the additional weight, W_(T)(n),to spatial orthogonalize the composite channel. Exemplary solutions forthese weightings are the joint SVD, the ZF and MMSE. The advantage ofthis approach is that the processing required to adapt all N SOP binmatrix channels may be substantially higher than the processingcomplexity to adapt the average TSP and RSP.

[0155] The rejection and prevention of interference can be accomplishedin conjunction with the space-frequency processing discussed above. Thisis especially useful when the number of spatial directions used forcommunication is less than the number of antennas. This case occurs whenweak spatial directions are not utilized or when the number of antennasat the receiver and transmitter are not the same. In either case, one orboth ends of the communication link have extra spatial degrees offreedom to use for the purpose of mitigating interference.

[0156] The amount of interference arriving at an antenna array can bequantified by the interference covariance matrix,

R _(I)(n)=E{I(n)I(n)^(H)},

[0157] where I(n) is the M_(R) length interference plus noise vectorreceived in SOP bin n. This matrix defines an undesired interferenceplus noise subspace in M_(R)-space for bin n. The interference plusnoise energy that contaminates a particular received subchannel symbolwith bin n and spatial direction m, is equal to,

u ^(H)(n,m)R _(I)(n)u(n,m),

[0158] where u(n,m) is the combining weight vector for the RSP(n,m). Anadvantageous interference rejection technique is then to “whiten” theeffect of the interference across the spatial directions, so that theinterference is minimized and spread evenly across all spatialdirections used. Therefore, each of the RSP weighting vectors aremodified by the matrix R_(I) ^(−½)(n),

u′(n,m)=u(n,m)R _(I) ^(−½)(n).

[0159] Alternatively, the RSP weighting vectors are the vectors of theoutput singular matrix, U′(n), from the SVD of the modified spatialchannel,

R _(I) ^(−½)(n)H(n)=U′(n)Σ′(n)V′(n)^(H).

[0160] Note that a very useful simplification of the above interferencerejection technique is to average the interference covariance matrixover all N bins and possibly a set of bursts to arrive at an averagespatial interference covariance matrix, R_(I), that is independent ofbin n. In this case, every RSP combining vector is modified in the sameway due to interference. This approach can significantly reduce theamount of computations needed to determine R_(I) and R_(I) ^(−½). Notethat it is often beneficial to add a scaled matrix identity term toestimates of the interference covariance matrix to reduce thesensitivity of these interference mitigation approaches to covarianceestimation errors.

[0161] Similar interference mitigation techniques can be advantageouslyemployed at the transmitter to reduce the amount of interferenceradiated to unintentional receivers. In the TDD channel, reciprocity inthe radio link allows the undesired receive interference subspace ineach SOP bin to be accurately used to describe the transmitter subspace.That is, the amount of interference transmitted to unintentionalreceivers is

v ^(H)(n,m)R _(I)(n)v(n,m),  60

[0162] where v(n,m) is the transmit weight vector for the TSW(n,m). Anoptimal interference reduction approach is then to minimize and “whiten”the transmitted interference across spatial directions. In the samefashion as the receiver case, the TSW vectors are modified by the matrixR_(I) ^(−½)(n). Alternatively, the TSP weight vectors are the vectors ofthe input singular matrix V′(n) from the SVD of the modified spatialchannel,

H(n)R _(I) ^(−½)(n)=U′(n)Σ′(n)V′(n)^(H).  61

[0163] Again, a significant simplification occurs when the interferencecovariance matrix is determined by averaging over frequency or SOP bins.It is especially advantageous to average over SOP bins in afrequency-division-duplex (FDD) system, where significant averaging ofthe receive convariance matrix results in a good estimate of thetransmit covariance, even though instantaneous channel reciprocity doesnot hold.

[0164] Interference rejection at the receiver and interference reductionat the transmitter are done together by simply combining the twotechniques outlined above. In this case, the RSP vectors and TSP vectorsare contained in the input and output matrices of the SVD of,

R _(I,R) ^(−½)(n)H(n)R _(I,T) ^(−½)(n).

[0165] As outlined previously, it can be advantageous to use the sameTSWs and RSWs for all bins. This approach can be combined withinterference mitigation by the determining the transmit and receiveweight vectors that maximize average power delivered to the receiver ofinterest, while at the same time, minimizing power delivered to otherundesired receivers. There are various optimization problems that can beposed to determine these TSP or RSP directions, each involving thedesired receiver covariance matrix and the undesired covariance matrix.For example, one TSP problem is${\max\limits_{v}{v^{H}R_{d}v\quad \text{such~~that}\quad v^{H}R_{I}v}} \leq {P_{I}\quad \text{and}\quad v^{H}v} \leq {P_{T}.}$

[0166] That is, a TSP direction is chosen for all SOP bins thattransmits the maximum amount of power to the desired receiver whilemaintaining a transmit power limit, P_(T), and a transmittedinterference limit, P_(I). For this particular problem, the TSPdirection is equal to the maximum generalized eigenvector of the matrixpair {R_(d),(R_(I)/P_(I)+I/P_(T))}. One example of an effectiveinterference rejecting RSP for all SOP bins is a weighing that maximizesthe average received SINR. The RSP that maximizes SIR is the maximumeigenvector of the matrix R_(I) ^(−½)R_(d)R_(I) ^(−½).

[0167] One further simplification to the above algorithm is to model theinterference and/or the desired covariance as diagonal, or nearlydiagonal. When both R_(d) and R_(I) are diagonal, the solution to theabove optimization problem reduces to the maximal ratio SINR combiner,u, and transmitter, v. It is also sometimes preferable to only considerother subsets of the elements of either the desired or interferencecovariance matrices.

[0168] One skilled in the art will also recognize that all the TSPs andRSPs can be used when there is only one SOP bin, such as a commonfrequency.

[0169] Space Frequency Coding

[0170] Many of the advantageous space frequency encoding techniquesembodied in the invention may be broadly classified in two exemplarycategories. The first category involves techniques wherein the spatialmatrix channel within each SOP bin undergoes space frequency processingat the transmitter, or the receiver or both, resulting in asubstantially independent set of one or more parallel communicationsubchannels within each SOP bin. The objective of the encoder anddecoder in this case is to appropriately allocate the transmittedinformation among multiple independent space-frequency subchannels usinginterleaving, power and bit loading, or both. The second category ofspace frequency encoding involves transmitting and receiving one or moresymbol sequences in each SOP bin using one or more transmitter andreceiver weight vector combinations that are not necessarily intended tocreate independent spatial subchannels within each SOP bin. This resultsin significant cross-talk between each symbol stream present at thereceiver output. A decoder then uses knowledge of the equivalent matrixchannel within each SOP bin, and knowledge of the set of possibleencoder sequences to estimate the encoder symbol sequence that gave riseto the cross-talk rich output SOP bin vector sequence. The maindifferentiating feature between the first approach and the secondapproach is the presence or lack of spatial processing that results insubstantially orthogonal spatial subchannels within each SOP bin. Bothapproaches have the advantageous ability to multiply the data rate thatcan be achieved in MIMO channels with multipath.

[0171] Coding for Substantially Orthogonal Space-Frequency Subchannels

[0172] In applications where the spatial channels are processed toachieve multiple substantially independent spatial subchannels withineach SOP bin, an advantageous embodiment of the invention involvesencoding the input data sequence into a digital symbol stream that isthen routed in various beneficial ways through the available parallelspace frequency subchannels. FIG. 22 depicts a preferred embodiment.This embodiment involves distributing the symbol outputs of a singleencoder among all of the available space frequency subchannels. Severalknown coding schemes that can be combined effectively with spacefrequency processing to distribute information transmission over thespace and frequency dimensions of a communication channel. Thisdiscussion assumes estimation of the MIMO channel by transmitting aseries of training symbol sequences from each antenna element asdiscussed herein. The discussion further assumes that the receiver andtransmitter either share the information required to decompose thechannel into parallel sub-channels, or the TDD techniques discussedherein are used to do the same.

[0173] Referring again to FIG. 22, the preferred embodiment exploits athree layer coding system. The first layer of coding includes thecombination of transmitter TSWs 210A through 210B, Transmitter SOPprocessors 190, receiver SOP processors 200, and receiver RSWs 220Athrough 220B. This first layer of coding performs the spatialprocessing. The second layer of coding includes a Trellis Encoder andInterleaver (420) at the transmitter in combination with a Deinterleaverand ML Detector 430 at the receiver. The third layer code involves ReedSolomon (RS) Encoder 410 at the transmitter in combination with an RSDecoder 440 at the receiver. The bit level RS coding occurs prior to thetrellis encoding and the Reed Solomon codeword detector acts upon thebit sequence from the ML detector. The fourth layer of coding involvesan ARQ code that recognizes Reed Solomon codeword errors at the receiverin the Receiver ARQ Buffer Control 450 and requests a codewordretransmission from the Transmitter ARQ Buffer Control 400. Theretransmission request is made through a Reverse Link Control Channel460. The reverse control channel is a well known radio system conceptand will not be discussed herein. This combination of coding techniquesand space frequency processing is preferable because it provides for arich combination of space and frequency diversity and it is capable ofobtaining very low bit error rates. The detailed operation of the RSencoder and decoder, as well as the ARQ system is well known to oneskilled in the art. Following this discussion, it will be clear to oneskilled in the art that other combinations of one or more of these fourcoding elements may be employed with advantageous results in variousapplications.

[0174] The trellis coding step may be substituted with CBM-QAM or aturbo code. Similarly, the Reed-Solomon code may be substituted with ablock code, or with an error checking code such as a CRC code. Thetransmitter end would then include the necessary encoder and thereceiver end would include the necessary decoder.

[0175] There are at least two basic methods for employing trellis codingto distribute information among substantially independent spacefrequency subchannels. One method is adaptive encoding that modifies thebit and power loading for each subchanel according to its quality. Thesecond method involves maintaining constant power and bit loading forall space frequency subchannels. Both of these methods are discussedbelow.

[0176] Space Frequency Trellis Coding with Orthogonal SpatialSubchannels and Adaptive Power and Bit Loading

[0177]FIG. 22 depicts the coding and interleaving detail for thetransmitter and receiver portions of the present embodiment. Encodingand Interleaving system 10 encodes the data into a set of complexsymbols. Each of the complex symbols is then allocated to a particulartransmitter TSW (210A through 210B). The input to each TSW forms avector of frequency domain symbols that are fed into the same bin of oneor more transmit SOP processors. Each transmitter TSW, possibly inconjunction with a receiver RSW converts the matrix channel within eachSOP bin into a set of substantially orthogonal space frequencysubchannels using one of the methods discussed herein.

[0178]FIG. 23 displays a more detailed diagram of the encoder andinterleaver. An Information Allocation Unit 360 assigns the bits and thetransmitter power that will be allocated to each space frequencysubchannel. One method for accomplishing this assignment is theso-called gap analysis. In this technique, a particular coset code withan associated lattice structure is characterized by first determiningthe SNR required to achieve a theoretical capacity equal to the desireddata rate. The code gap is then the SNR multiplier required to achievethe target probability of error at the desired data rate. In a parallelchannel communication system, this gap can be used to determine thepower and bit distributions that maximize data rate subject to aprobability of error constraint. With a coding gap of a, the ratemaximizing water-filling solution for the space frequency subchannelsbecomes${{p\left( {n,m} \right)} = \left( {\xi - \frac{\sigma_{n}^{2}\alpha}{{{\lambda \left( {n,m} \right)}}^{2}}} \right)^{+}},$

[0179] where σ_(n) ² is the noise power and m is the spatial index and nis the DFT frequency index.

[0180] The bit allocation per sub-channel is then given by${b\left( {n,m} \right)} = {\log \quad {\left( {1 + \frac{{p\left( {n,m} \right)} \cdot {{\lambda \left( {n,m} \right)}}^{2}}{\alpha \quad \sigma_{n}^{2}}} \right).}}$

[0181] After the power and bit loading assignments are accomplished inthe Information Allocation Unit, the bits are encoded with a TrellisEncoder 370. It is not possible to achieve infinite bit resolution(granularity) with coset codes. Therefore the gap analysis solutionshould be modified. Several bit loading algorithms exist to resolve thisproblem. One method involves rounding down the water filling solution tothe nearest available quantization. The granularity of possible bitallocations is determined by the dimensionality of the coset codelattice structure. In the MIMO channel communication structuresdescribed herein, the orthogonal constellation dimensions are thecomplex plane, space, and frequency.

[0182]FIG. 26 illustrates an example of a practical method for bitloading with a trellis encoder that uses a one dimensional QAM symbolconstellation. The bit load is adjusted down for a given trellis encoderoutput symbol by assigning a number of fixed zeros to one or more of theinput bits to the encoder. FIG. 26 shows the operation of the trellisencoder and the trellis state diagram for the decoder for foursuccessive symbol transmissions. Four bits are assigned to the firstspace frequency subchannel. A first subchannel trellis encoder input 350is assigned 4 bits so Symbol 1 can take on any one of 32 values. Thereare two bits feeding the convolutional encoder, and two bits feeding thecoset select. The ML detector at the receiver uses the trellis statediagram and the channel state information to solve the maximumlikelihood recursion. This is efficiently accomplished with the Viterbialgorithm. The trellis code state diagram defines a set of symbolsequence possibilities {Z}. The space frequency subchannel is denotedĤ(n,k), for SOP bin n at burst k. The maximum likelihood equation isthen given by$\left\{ {{\hat{z}(1)}^{T},{\hat{z}(2)}^{T},\cdots \quad,{\hat{z}(N)}^{T}} \right\} = {\arg \left\{ {\min\limits_{z = {\{{{z{(1)}}^{T},{z{(2)}}^{T},\cdots \quad,{z{(N)}}^{T}}\}}}{\sum\limits_{n = 1}^{N}{{{{\hat{H}\left( {n,k} \right)}{z(n)}} - {x\left( {n,k} \right)}}}^{2}}} \right\}}$

[0183] where z(n) is the symbol hypothesized for SOP bin n. The decoderoutput state diagram for first space frequency subchannel 340 includesfour possible parallel transitions for each trellis branch and all ofthe trellis branches are possible. The second space frequency subchannelin the sequence is assigned three bits so a second trellis encoder input352 shows one bit fed into the coset select with two bits still feedingthe convolutional encoder. A decoder state diagram 342 for the secondspace frequency subchannel has only two parallel transitions for eachtrellis branch but still maintains all trellis branch possibilities.Continuing in succession, a third space frequency subchannel is assignedonly two bits to an encoder input 354 so there are no paralleltransitions considered by a trellis decoder state diagram 344. In afourth space frequency subchannel, only one bit is assigned to anencoder input 356 so there are no parallel transitions and some of thetrellis state branches (346) are no longer considered by the decoder. Itis understood that FIG. 26 is provided as a graphical aid and is notintended to represent an actual design.

[0184] The maximum Euclidean distance error sequence design metric isone preferable choice for a trellis encoder used with the parallel spacefrequency channel with this bit and power loading embodiment of theinvention. Other code error sequence design metrics that areadvantageous in various application conditions include product distanceand periodic product distance.

[0185] Referring again to FIG. 23, the output of the encoder isinterleaved across the various space frequency subchannels usingInterleaving block 260. Typically, the interleaving process distributesthe symbols so that symbols that are near one another at the encoderoutput are well separated in both the SOP bin assignment and the spatialsubchannel assignment. This distributes the effects of channelestimation errors and localized frequency domain or spatial domaininterference so that the decoder error is reduced. It is understood thatthe bit and power assignments by Information Allocation block 360 takeplace with knowledge of the post-interleaved channel strength. It isunderstood that the encoding and decoding process can begin and endwithin one burst, or it may take place over a multitude of bursts.

[0186] One skilled in the art will recognize that a multitude of lesssophisticated adaptive power and bit loading algorithms can beadvantageously applied to a substantially independent set of spacefrequency subchannels. One example is an algorithm wherein a spacefrequency subchannel is either loaded with maximum power or no power andthe bit distribution may be adjusted in only two increments.

[0187] A second alternative embodiment shown in FIG. 19 includes oneencoder for each SOP bin, with the output symbols of each encoderallocated among several spatial subchannels. A third embodiment shown inFIG. 20 involves one encoder for each spatial subchannel, with theoutput symbols of each encoder distributed among the SOP bins for thatspatial subchannel. A fourth embodiment shown in FIG. 21 involves aseparate encoder for each available space frequency subchannel.

[0188] It will be clear to one skilled in the art that the channelestimation tools taught herein are very useful in improving the accuracyof the channel estimates used for the bit loading and decoding process.

[0189] One skilled in the art will recognize that many of the othercoding techniques for parallel sub-channel bit loading communicationsystems, not mentioned here, can also be applied to the presentinvention.

[0190] Space Frequency Trellis Coding with Orthogonal SpatialSubchannels and Flat Power and Bit Distribution

[0191] In some cases it is difficult to adaptively load the power andbit assignments for each available space frequency subchannel. Forexample, the transmitter and receiver may not be able to adapt theloading fast enough to accommodate time domain variation in the channel.In another example, the required feedback from the receiver to thetransmitter requires a significant portion of the available reverse linkbit rate. Adaptive bit loading may also be overly complicated forcertain applications. Thus, it is often advantageous to encode anddecode a symbol stream in such a manner that the power and bitallocation is constant for all space frequency subchannels. This iseasily accomplished by employing the embodiments depicted in FIGS. 22-23, and assigning a constant power and bit allocation to all spacefrequency subchannels in the Information Allocation block 360.

[0192] Space Frequency Coding Without Orthogonal Spatial Subchannels

[0193] In applications where the spatial channels are not processed toachieve substantially orthogonal spatial subchannels within each SOPbin, an advantageous embodiment of the invention involves utilization ofa vector maximum likelihood decoder in the receiver to decode a symbolsequence that includes multiple symbols per SOP bin. The vector maximumlikelihood detector is capable of determining the transmitted symbolvector in each SOP bin even in the presence of spatial subchannels thatcontain significant cross-coupling between the channels. The vectormaximum likelihood detector uses an estimate of the matrix channel fromeach SOP bin to decode a sequence of groups of symbols with one groupfor each SOP bin. The groupings will be referred to here as amultidimensional symbol vector, or simply a symbol vector. The MLdetector uses an estimate of the matrix channel that exists in each SOPbin to find the most likely sequence of transmitted encoder vectorsymbols.

[0194]FIG. 24 depicts a transmitter system wherein multiplespace/frequency subchannels are employed without spatialorthogonalization. FIG. 25 depicts a receiver system for thisapplication.

[0195] The bit sequence b(k) is encoded into a sequence ofmultidimensional symbol vectors in a Bit to Symbol Encoding block 250.Each output of the encoder is an M₀ by 1 complex symbol vector, where M₀is the number of spatial directions that will be used for transmission.Note that M₀ is preferably chosen to be less than or equal to M_(T). Apreferable construction of the encoder is a multidimensional trellisencoder. One advantageous metric for designing the trellis encoderconstellation and convolutional encoder polynomial will be providedbelow. Within the previously discussed Symbol Interleaver block 260, thevector symbol sequence is demultiplexed and interleaved with a SymbolSequence Demultiplexor 300 and a Transmit Symbol Routing block 310.Transmit Symbol Routing block 310 interleaves the vector symbol sequenceso that the elements of a given vector symbol are grouped together andtransmitted in one SOP bin. Thus, different vectors are separated by amultitude of SOP bins before transmission, but all elements within thevector symbol share the same SOP bin. The purpose of the interleaver isto distribute the vector symbol sequence so that the fading present inthe matrix channels within the SOP bins is randomized at the output ofthe receiver interleaver. The decoder can recover information associatedwith symbols that are transmitted through SOP bins that experience adeep fade, provided that the adjacent symbols do not also experience thesame fade. Since there is often a high degree of correlation in thefading experienced by adjacent SOP bins, the interleaver makes thefading more random and improves decoder error performance. Afterinterleaving, each element of a vector symbol is assigned to one antennafor the SOP bin assigned to that vector symbol. Transmitter SOPprocessors 190 perform the transmitter portion of the SOP.

[0196] After the transmitter SOP, it is often advantageous to performspatial processing with TSP 230. It is understood that the matrixrepresenting the operation of TSP 230, i.e., the Transmitter WeightMatrix, may also be an identity matrix so that no weighting isimplemented. It can be beneficial to choose a number of spatialdirections that is less than the number of transmitter antennas. In thiscase, the Transmitter Weight Matrix increases the dimensionality of thetime domain vector sequence from the SOP bank. As an example of when itis advantageous to choose a subset of the available transmitter spatialdirections, if the receiver has fewer antennas than the transmitter,then it is known that the information capacity of the matrix channelswithin each SOP bin will not support a number of parallel informationsubchannels that is greater than the number of receive antennas. Thisimplies that the number of symbols in each transmitted symbol vector,and hence the number of transmitted spatial directions, should not begreater than the number of receiver antennas. As another example, in aRayleigh fading channel, the smallest singular values of an M_(R) byM_(T) matrix channel are on average much weaker than the largestsingular value. This implies that the average information capacitycontained in the smallest singular value may not justify the extrasignal processing complexity required to transmit over that dimension.In both of these cases, it is advisable to choose an advantageous subsetof the available transmit spatial directions.

[0197] The transmitter may not have knowledge of the individual channelmatrices within each SOP bin but may have knowledge of the covariancestatistics of the channel matrices, averaged over frequency, or time, orboth. In such cases, the Transmitter Weight Matrix can be optimized toselect one or more spatial directions that maximize the average receivedpower for the chosen number of spatial directions. The procedure foroptimizing the Transmitter Weight Matrix for this criteria is defined byEquations 50 to 52 and the associated discussion. This is one preferredmethod of selecting an advantageous set of spatial directions for theTransmitter Weight Matrix. Another advantageous criteria for selectingthe transmitter spatial directions is to maximize average received powersubject to constraints on the average interference power radiated tounintentional receivers. The procedure for optimizing the TransmitterWeight matrix for this criterion is defined by Equations 60 and 61 andthe associated discussion.

[0198] After the time domain signal is spatially processed, the signalis upconverted to the RF carrier frequency using Modulation and RFSystem 40 before being radiated by Transmit Antennas 51. Referring nowto FIG. 25, at the receiver the signal is downconverted and digitized byReceive Antennas 111 and Demodulation and RF System blocks 120. The RSP240 may then be used to process the time domain signal. The operation ofRSP 240 may be characterized by a Receiver Weight Matrix which may be anidentity matrix. One embodiment involves optimizing the RSP weights toreduce the number of received signals from M_(R) to M₀, which is thenumber of elements in the transmitted symbol vector and is also thenumber of transmitted spatial directions. In this case, the ReceiverWeight Matrix can be optimized to increase the average signal power ineach received spatial direction. The optimization procedure toaccomplish this is defined by Equations 50 to 53 and the associatedtext.

[0199] Channel ID block 130 is used to estimate the matrix channel ineach SOP bin. Procedures for channel estimation are described below.Channel state information for each SOP bin is fed into a Symbol to BitDetector 280 which decodes the symbol sequence after it is passedthrough a Symbol Deinterleaver 270.

[0200] At the receiver, after de-interleaving the SOP bins, thespace-frequency sequence is again converted into a serial symbol streamby Demultiplexor 300. For a given set of spatio-temporal vector symbolsequence possibilities {Z}, and an estimate, Ĥ(n,k), of the channelmatrix in each SOP bin n at burst k, the maximum likelihood detector isgiven by equation (70):$\left\{ {{\hat{z}(1)}^{T},{\hat{z}(2)}^{T},\cdots \quad,{\hat{z}(N)}^{T}} \right\} = {\arg \left\{ {\min\limits_{z = {\{{{z{(1)}}^{T},{z{(2)}}^{T},\cdots \quad,{z{(N)}}^{T}}\}}}{\sum\limits_{n = 1}^{N}{{{R_{I}\left( {n,k} \right)}^{- \frac{1}{2}}\left( {{{\hat{H}\left( {n,k} \right)}{z(n)}} - {x\left( {n,k} \right)}} \right)}}_{2}^{2}}} \right\}}$

[0201] where z(n) is the vector representing the code segmenthypothesized for SOP bin n, and R_(I)(n,k) is the estimated noise plusinterference covariance matrix for SOP bin n and time k. This equationcan be solved efficiently using a vector ML detector. The SOP binchannel matrix estimates are understood to include the effects of theTransmitter Weight Matrix and the Receiver Weight Matrix. It isunderstood that the noise pre-whitening step in the ML detector costfunction can be substituted by a bank of RSPs that perform theinterference whitening as described herein.

[0202] In a Rayleigh fading channel, a desirable metric for designingthe trellis code is given by the product of a sum involving the two-normof vector segments of the trellis code error sequence:$\prod\limits_{n = 1}^{q}{{e(n)}}_{2}^{2}$

[0203] where q is the number of SOP bins in the error sequence, and e(n)is the vector difference between the true multi-dimensional code symbolsegment and the incorrect multi-dimensional symbol code segment for SOPbin n. This code design metric is a generalization on the conventionalproduct distance metric which contains a scalar error entry in theproduct equation while the new code design metric contains a vector twonorm entry in the product equation. It should now be evident that themultidimensional encoder can be realized by either directly producing avector consisting of a multidimensional QAM symbol with the encoderoutput or by grouping complex QAM symbols from a one dimensional encoderoutput into a vector. The vector symbol encoder alternative is preferredin some cases because this approach provides for a larger metric searchresult and hence a better fading code. After deinterleaving, the decoderthat is used at the receiver searches over all possible multidimensionalsymbols within each SOP bin to maximize Equation 70. It is understoodthat one skilled in the art will recognize after this discussion thatother desirable metrics such as Euclidean distance metrics, metricsdesigned for Rician fading channels, periodic product distance metrics,and others are straightforward to construct and space-frequency codescan then be determined through well known exhaustive search techniques.

[0204] In either the one dimensional encoder case, or themultidimensional encoder case, the encoder constellation selection andcode polynomial search to maximize the metric can be carried out using anumber of well known procedures.

[0205] It is possible to improve the performance of the space-frequencycoding system described above by using a number of transmitter antennas,or a number of receiver antennas, that is greater than the number ofsymbols transmitted in each SOP bin. If the number of receiver antennasis greater than the number of symbols in each SOP bin, then simplyapplying the approach described above is advantageous. If the number oftransmitter antennas is greater than the number of symbols transmittedin each SOP bin, then the techniques embodied in Equation 70 areadvantageous.

[0206] Channel Identification

[0207] The operation of Channel Identification block and Training SymbolInjection block will now be described. The transceiver should determinethe MIMO channel in order to form the TSWs and RSWs. For coherentspatial processing and detection, the receiver should obtain an estimateof the channel. We wish to identify the set of matrix channels thatresults after processing by the transmitter and receiver portions of anSOP. The notation for this channel is H(n) ∀n where n is the SOP binindex. Channel identification techniques embodied herein can be appliedto several preferable SOP pairs including the IFFT-FFT with cyclicprefix, the multiband filter bank, or any other of a number ofwell-known SOPs. The following exemplary channel identification approachexploits the correlated frequency fading across and possibly thecorrelated time fading in the channel. The correlation in the frequencydomain arises due to the limited time delay spread of the multipathchannel. The correlation in time is due to the fact that the channel,while time-varying, is driven by band-limited Doppler frequenciescreated by objects, which can include the transmitter and/or receiver,moving in the physical environment.

[0208] The wireless link is bidirectional, therefore each end of thelink should estimate not only a receive channel, but also a transmitchannel. For example, a base station should estimate both an uplink anddownlink channel. In systems which employ time division duplexing (TDD),electromagnetic reciprocity implies the receive and transmit propagationenvironments are the same, allowing the transmit channel to be estimatedfrom the receive channel. However, the transmit and receive electronicresponses are not necessarily reciprocal, and because the net channelresponse includes the electronics, a calibration procedure should beused to account for these differences. This calibration procedureprovides for matching in the amplitude and phase response between themultiple transmitter and receiver frequency converters. Several TDDcalibration procedures are known in the prior art and will not bediscussed herein.

[0209] In systems employing frequency division duplexing (FDD), thepropagation medium is not reciprocal; however, the paths' angles andaverage strengths are the same for transmit and receive. This enablesthe use of subspace reciprocity, but incurs a more rigorous calibrationrequirement. The FDD calibration should insure subspace reciprocitywhich requires that the array response vector at a given angle onreceive is proportional to the corresponding vector on transmit. Thisrequirement is satisfied by again calibrating the amplitude and phasedifferences among the multiple transmit and receive frequency converterchannels and by matching the transmit and receive antenna elementresponse as well as the array geometry.

[0210] An alternative approach to transmit channel estimation in FDDsystems uses feedback. The transmit channel is measured by sendingtraining symbols to the receiver, which records the amplitude induced bythe training symbols. Using receiver to transmitter feedback on aseparate feedback control channel, the training responses are sent backto the transmitter. The transmitter, knowing the training excitations itused and the corresponding responses through feeedback, the forwardchannel can be estimated.

[0211] In general, channel identification can be done either with orwithout training. A desirable channel identification algorithm should berobust to and operate in a variety of modem implementations. Apreferable MIMO channel identification technique operates with embeddedtraining inserted into the data stream by Training Symbol Injectionblock 20 in each burst. In this case, both data symbols and trainingsymbols may be transmitted within a single burst. Furthermore, thechannel can be determined in one burst, or filtering training datagathered over multiple bursts. Being able to update the channelestimates after every received burst makes the overall communicationsystem robust to time variation in the channel. In addition, frequentchannel estimates reduce the destructive effects of imperfect carrierfrequency recovery. Since imperfect carrier recovery imparts a phaseshift to the channel that continues to grow with time, shortening thetime between channel estimation events keeps the channel estimationinformation from becoming “stale”. Note, however, any of the well knownblind channel estimation techniques can be used to determine thetraining symbol outputs as an alternative to using training. However,adaptive blind training is more prone to generating burst errors.

[0212] The parameters to be identified are the N MIMO spatial channelmatrices. Hence, there are N·M_(R)·M_(T) complex elements to bedetermined,

H _(i,j)(n), ∀n∈[1,N], ∀i∈[1,M _(R) ], ∀j∈[1,M _(T)].

[0213] By exploiting whatever correlation exists across the SOP bins, itmay be possible to reduce the amount of overhead required to identifythe channel. The amount of correlation that exists across SOP bins isdetermined by the specific implementation of the SOP. If the SOPimplementation includes the IFFT-FFT pair, and the length of the FIRchannel is time limited with ν<<N, then a relatively large degree ofcorrelation exists across the SOP bins.

[0214] In certain embodiments of the invention, the desired techniqueshould identify the MIMO channel on a burst-by-burst basis, such asthose with rapidly time-varying channels. This implies that trainingdata should be included in every burst. If the throughput of informationis to be maximized, the amount of training data in each burst should beminimized. It is therefore useful to determine the minimum amount oftraining data required, per burst, that allows full characterization ofthe channel by the receiver. It turns out that the minimum number oftraining symbols required to sufficiently excite the MIMO channel forestimation with an OFDM SOP is M_(T)ν. To understand this result,consider the identification of a SISO channel, where each of the Nvalues of the vector H_(i,j) should be found. These N values are notindependent since, ${H_{i,j} = {{Y\begin{bmatrix}h \\0\end{bmatrix}} = {X \otimes^{- 1}Z}}},$

[0215] where X is a vector of all SOP bin outputs for antenna i, Z is avector of bin inputs for antenna j, and h is a vector of the time-domainFIR channel from antenna j to antenna i. The matrix operator {circleover (x)}⁻¹ represents element by element divide. Since the time-domainchannel is time limited to ν samples, only ν values of the transmittedsymbols, Z, need to be training values. Furthermore, the identificationof the SIMO channel only requires the same set of ν transmitted trainingtones, since each SISO component in the SIMO channel is excited by thesame input data. In a system embodiment with multiple inputs (M_(T)>1),identification of the MIMO channel requires the identification of M_(T)separate SIMO channels. Hence, only M_(T)ν training symbols are neededto sufficiently excite the MIMO channel for channel identification.

[0216] MIMO Identification

[0217] The identification of the MIMO channel is accomplished byseparately exciting each of the transmit antennas that will be used forcommunication. This decomposes the MIMO identification problem intoM_(T) SIMO identification problems. In order to accomplish channelidentification in a single burst, M_(T) mutually exclusive sets of νbins are selected from the N available bins to carry training symbols.Each transmitter antenna carries training symbols in a unique one of theM_(T) sets of bins, while transmitting no energy in the bins containedin the union of the remaining M_(T)−1 sets of ν bins. This isaccomplished by choosing the TSWs 210A-C that correspond to trainingbins such that a single entry in the vector is “1” and the remainingentries equal to “0”. It is the j^(th) entry of a TSW that is set equalto “1” for those training symbols which are to be transmitted from thej^(th) antenna. For example, say that symbol bin n=2 is one of thetraining bins associated with transmit antenna 3. Then,

TSW(2,1)=[0 0 1 0 . . . 0]^(T), and TSW(2,m)=0 for ∀m≠1,

[0218] and the corresponding training symbol z(2,1). By examining thecontents of each set of training bins separately, the MIMO channelresponse is determined by finding M_(T) independent SIMO channelresponses.

[0219] In embodiments in which rapid updates of the channel estimate isnot required, another exemplary training scheme may be employed. Thistraining scheme involves using just one set of ν training bins. On agiven burst, one of the transmit antennas sends training symbols in thetraining bins and the other antennas transmit no energy in those bins.This allows the receiver to identify one of the M_(T) SIMO channels. Onthe next burst, a different antenna sends training symbols in thetraining bins while the other antennas transmit no energy in those samebins. The receiver is then able to identify another set of N SIMOchannels. This procedure is repeated until training data has been sentby each of the transmit antennas, allowing the entire MIMO channel to beidentified. The entire procedure is repeated continuously so that fullchannel is determined every M_(T) bursts.

[0220] SIMO Channel Identification

[0221] We have just shown that identification of the MIMO channel can beaccomplished by successive identification of each SIMO channel. It istherefore useful to discuss specific techniques for obtaining a SIMOchannel response. The following discussion assumes that the SOP is theIFFT-FFT pair. Channel identification techniques for other SOPs thatexploit frequency and possibly time correlation in the similar fashionwill be obvious to one skilled in the art.

[0222] It is assumed that a certain subset of available SOP bins areallocated for training. Let J be this set of frequency bins used forlearning a SIMO channel. To begin, assume that J contains ν bin indices.Furthermore, let Z_(t) be the ν training symbols and X_(t,i) be thereceived data in the training frequency-bins from antenna i. Let thequantities ĥ_(i), Ĥ_(i) be the estimated time-domain andfrequency-domain channels from the transmit antenna under considerationto the receive antenna i. In other words, ĥ_(i) is the ν-length impulseresponse from the input under consideration to output i. Likewise, Ĥ_(i)is a vector of N frequency domain values for this channel. With thesedefinitions, it can be shown that

ĥ _(i) =Y _(j,{overscore (ν)}) ⁻¹(X _(t,i) {circle over (x)} ⁻¹ Z_(t)),  (81)

[0223] and

Ĥ_(i)=Y_({overscore (N)},{overscore (ν)})ĥ_(i).  (82)

[0224] where,

{overscore (ν)}={1,2, . . . ν},

{overscore (N)}={1,2, . . . N},

[0225] and${Y_{PQ} = {\frac{1}{\sqrt{N}}^{{- j}\quad 2\pi \quad {{pq}/N}}}},{\forall{p \in \left\{ P \right\}}},{\forall{q \in {\left\{ Q \right\}.}}}$

[0226] This also generalizes to any number of training tones, γ, inwhich case the set J includes γ bin indices. When γ≧ν, the frequencydomain channel can be determined by,

Ĥ _(i) =Y _({overscore (N)},{overscore (ν)}() Y _(J,{overscore (ν)})^(H) Y _(J,{overscore (ν)}))⁻¹ Y _(j,{overscore (ν)}) ^(H)(X _(t,i){circle over (x)} ⁻¹ Z _(t)).  (83)

[0227] Note that many of the above calculations can be performed inadvance if the training bins are predetermined and fixed. Then, thematrix Y_({overscore (N,ν)})(Y_({overscore (ν)},Γ) ^(H)Y{overscore(ν)},Γ)⁻¹Y_({overscore (ν)},Γ) ^(H) can be computed and stored.

[0228] Note that there is no requirement that the training symbolsalways reside in the same bins from burst to burst. As long as thetransmitter and receiver both know where the training symbols are placedin any given burst, the training bins may be varied from one burst tothe next. This may be useful to characterize the nature of colored(across SOP bins) noise and/or interference are present.

[0229] A highly advantageous simplification of (83) can be done when νtraining symbols are placed in bins that are evenly spaced throughoutthe burst. In other words,$J = {\left\{ {0,\frac{N}{v},\frac{2N}{v},\cdots \quad,\frac{\left( {v - 1} \right)N}{v}} \right\}.}$

[0230] In this case, Y_(J,{overscore (ν)}) ⁻¹ is equal to the ν-pointIFFT matrix so that equation (81) represents the execution of an ν-pointIFFT. One may then obtain Ĥ_(i) in equation (82) by performing anN-point FFT on a vector consisting of ĥ_(i) padded with N−ν zeros. Thisapproach to identifying Ĥ_(i) is only of computation order (N+ν)log₂ν.

[0231] Identification Over Multiple Bursts

[0232] Identification accuracy can be improved by either increasing thenumber of training symbols within each burst or by averaging overmultiple bursts if the channel is correlated from one burst to another.Some degree of time domain correlation exists in the channel because theDoppler frequency shifts caused by moving objects in the physicalenvironment are band-limited. This time correlation can be exploited byrecursively filtering the estimated channel from the present burst withchannel estimates from previous bursts. A general filtering approach isrepresented by

{tilde over (h)}(k+1)=F(k){tilde over (h)}(k)+G(k)ĥ(k)

[0233] where {tilde over (h)} is the smoothed channel estimate of ĥ overbursts k. The particular recursive filter weights F(k) and G(k) can bederived in a number of fashions. Two exemplary filtering methods aregiven in the following. The first approach determines a time-invariantFIR filter for each element of h based on a MMSE cost function. Thesecond design is time-varying Kalman filter.

[0234] A particularly simple, yet effective, filter design technique isthe determination of a time-invariant FIR filter, w, that minimizes theMMSE between the true channel impulse response and the filteredestimate. This design approach is referred to as Wiener filtering. Inthis embodiment, independent fading is assumed on each element of thechannel impulse response. Therefore, each element of h can be consideredindependently. An FIR filter produces a filtered estimate by forming aweighted sum of the previous p+1 estimates for that particular impulseresponse element,${{{\overset{\sim}{h}}_{i}(k)} = {w^{H}\begin{bmatrix}{{\hat{h}}_{i}(k)} \\\vdots \\{{\hat{h}}_{i}\left( {k - p} \right)}\end{bmatrix}}},{{\forall i} = 1},2,\ldots \quad,{v.}$

[0235] Using ν such identical filters for each element of the impulseresponse, then the filtered estimate is given by {tilde over(h)}(k)=[{tilde over (h)}_(i)(k) . . . {tilde over (h)}_(ν)(k)]^(T). TheWiener filter solution for w satisfies the following equation,${\min\limits_{w}{E\left( {{{w^{H}{\hslash_{i}(k)}} - {h_{i}(k)}}}^{2} \right)}} = {\min\limits_{w}{{E\left( {{{w^{H}\begin{bmatrix}{{\hat{h}}_{i}(k)} \\\vdots \\{{\hat{h}}_{i}\left( {k - p} \right)}\end{bmatrix}} - {h_{i}(k)}}}^{2} \right)}.}}$

[0236] The solution for the above optimization problem is given by,

w=[E(

_(i)(k)

_(i)(k)^(H))]⁻¹ E[

_(i)(k)h _(i)(k)]=R

_(i) ⁻¹ R

_(i) _(h) _(i) .

[0237] If each delay in the channel impulse response undergoes Raleighfading is assumed then,$R_{\hslash_{i}} = {{\sigma_{h}^{2}\begin{bmatrix}{J_{0}(0)} & {J_{0}\left( {{\omega \left( {N + v} \right)}T} \right)} & \cdots & {J_{0}\left( {{\omega \left( {N + v} \right)}T} \right)} \\{J_{0}\left( {{\omega \left( {N + v} \right)}T} \right)} & ⋰ & \quad & \vdots \\\vdots & \quad & ⋰ & \quad \\{J_{0}\left( {\omega \quad {p\left( {N + v} \right)}T} \right)} & \cdots & \quad & {J_{0}(0)}\end{bmatrix}} + {\sigma_{e}^{2}I}}$ and${R_{\hslash_{i}h} = {\sigma_{h}^{2}\begin{bmatrix}{J_{0}(0)} \\{J_{0}\left( {{\omega \left( {N + v} \right)}T} \right)} \\\vdots \\{J_{0}\left( {\omega \quad {p\left( {N + v} \right)}T} \right)}\end{bmatrix}}},$

[0238] where T is the sampling rate, ω is the maximum Doppler frequency,and J₀ is the zeroth-order Bessel function. The quantities σ_(h) ² andσ_(e) ² are the average channel power and the channel estimation noisepower, respectively.

[0239] This filtering approach has many advantages. First, it iscomputationally simple. Each coefficient of the channel impulse responseis filtered independently with a constant, precomputed FIR weighting.Second, the underlying time-correlation in the multipath fading channelis efficiently exploited. Third, the exact values used for the filterare optimal in a MMSE sense.

[0240] A more generalized time-varying filtering approach is nowdeveloped based on the Kalman filtering equations. A general model forthe time-correlated nature of the channel impulse response is given bythe following set of equations,

f(k+1)=Af(k)+q(k)

{tilde over (h)}(k)=Cf(k)+r(k)

[0241] where the q and r represent noises with covariances Q and R,respectively. The matrices A,C,Q,R are used to define the particularmodel for the correlation of the impulse response over bursts. Note thatthe vector {tilde over (h)} can also include the impluse responsecoefficients for more than one receive antenna. In this case, the abovemodel can include both time correlation and correlation across space.

[0242] In a multi-access scheme, successive channel identifications mayoccur at an irregular rate. In this case, this Kalman filter approach isparticularly useful since the filtering can be done with measurementupdates and time updates,

{circumflex over (f)}(k+1)=A(I−L(k)C){circumflex over (f)}(k)+AL(k)ĥ(k)

L(k)={circumflex over (P)}(k)C ^(H)(C{circumflex over (P)}(k)C ^(H)+R)⁻¹

{circumflex over (P)}(k)=A(I−L(k)C){circumflex over (P)}(k)A ^(H) +Q

{tilde over (h)}(k)=C{circumflex over (f)}(k)

[0243] where L(k)=0 when the receiver is not receiving data in thepresent burst.

[0244] Interference Subspace Identification

[0245] For many of the spatial processing techniques embodied in thisinvention, the operation of the TSP and RSP can depend, in part, on thelevel of interference present in the wireless environment within whichthe invention operates. More specifically, it may be preferable toreduce the amount of interference contributed to other receivers by ajudicious choice of the TSWs. It may also be preferable to improve thesignal quality at the receiver by using RSWs that reject interference.In these cases, some quantitative measure of the interference acrossspace and frequency is needed.

[0246] One preferable measure of the interference present is theso-called interference spatial covariance matrix, which describesinterference correlation across space for each frequency bin,

R _(I)(n)=E[I(n)I(n)^(H)]  (1)

[0247] where x, (n) represents an M_(R)-length received vector ofsignals from the interfering transmitter(s). To be more precise,R_(I)(n) describes the interference and noise correlation across spacefor each frequency bin. Since we assume that the noise at the output ofeach receiver antenna path is additive thermal noise, and therefore thatthe additive noise is uncorrelated between any two antenna outputs, thenoise contribution to R_(I)(n) is non-zero only on the matrix diagonal.In environments dominated by interference, i.e. the interference powerat the receiver is much stronger than the additive receiver noise, thenoise contribution to R_(I)(n) can be neglected. The interferencecovariance matrix contains information about the average spatialbehavior of the interference. The eigenvectors of this matrix define theaverage spatial directions (in M_(R)-space) occupied by theinterference. The eigenvalues of the matrix indicate the average poweroccupied by the interference in each the eigendirection. Theeigendirections that are associated with large eigenvalues indicatespatial directions that receive a large amount of average interferencepower. The eigendirections associated with small eigenvalues indicatespatial directions that are preferable in that they receive less averageinterference power.

[0248] Identifying the receive covariance matrix, R_(I)(n), is requiredfor finding preferable RSPs. An analogous transmit covariance matrix isrequired for finding preferable TSPs. Notice that we've defined R_(I)(n)in terms of received signal samples in Equation (1). Since the receivedsignal samples are not usually available at the transmitter, it ispreferable to derive the transmit covariance matrix from the receivecovariance matrix. In time division duplex (TDD) systems, the receiveand transmit covariance matrices are substantially equal when the timebetween reception and transmission is short relative to the rate of timevariation in the channel. In frequency division duplex (FDD) systems,the transmit and receive channel values are generally not correlatedwith one another at any given instant in time. However, the transmit andreceive covariance matrices are substantially equal in FDD systems whensufficient time averaging is used in the calculation of R_(I). There aremany techniques for determining the interference covariance matrix, twoof which are discussed below.

[0249] One interference characterization approach simply averages thereceived antenna signals during time periods in which the desiredtransceiver is not transmitting information. Since there is no desiredsignal arriving at the receiver, the interference (and noise) covarianceis precisely equal to the measured sample covariance matrix,${{\hat{R}}_{I}(n)} = {{{\hat{R}}_{x}(n)} = {\frac{1}{k_{2} - k_{1}}{\sum\limits_{j = k_{1}}^{k_{2}}{x\left( {n,j} \right){\left( {x\left( {n,j} \right)} \right)^{H}.}}}}}$

[0250] In TDD systems, one can make use of “dead-time” to collectsamples from the receiver during which time no energy from thetransmitting end arrives at the receiver. The “dead-time” isapproximately equal to the round trip propagation delay between the toends of the wireless communications link, and occurs when a transceiverswitches from transmission mode to reception mode. In the aboveequation, k₁ and k₂ are the burst indexes corresponding to the first andlast bursts received during the dead time. Thus, the interferencecovariance can be estimated with no increase in overhead.

[0251] The interference covariance matrices can also be determined whilethe desired signal is being transmitted to the receiver. One approachinvolves first determining the interference signal and subsequentlyfinding the interference signal covariance. The estimated receivedinterference is formed by subtracting the estimated desired signal fromthe total received signal,

[0252]Î(n,k)=x(n,k)−Ĥ(n,k){circumflex over (z)}(n,k).

[0253] Therefore, once the channel is identified and the informationsymbols determined, the remaining signal is considered to beinterference. The interference covariance matrix for bin n, averagedover K bursts is given by,${R_{I}\left( {n,k} \right)} = {\frac{1}{K}{\sum\limits_{j = {k - K + 1}}^{k}{{\hat{I}\left( {n,k} \right)}{\left( {\hat{I}\left( {n,k} \right)} \right)^{H}.}}}}$

[0254] It is understood that when estimating the covariance matrix, itmay be desirable to filter the covariance matrix estimates. It may alsobe advantageous in certain embodiments to determine an averageinterference covariance matrix across SOP bins. For example, within amultiple access system bursts may only be received occasionally, makingit difficult to acquire a sufficient number of bursts with which to forman accurate covariance matrix for each bin. So instead of averaging overtime (a series of received bursts), a covariance matrix is formed byaveraging over the SOP bins of a single burst,${R_{I}(k)} = {\frac{1}{N}{\sum\limits_{n = 1}^{N}{{\hat{I}\left( {n,k} \right)}{\left( {\hat{I}\left( {n,k} \right)} \right)^{H}.}}}}$

[0255] It may also be preferable to estimate the interference covariancematrices in an alternate frequency band. This can be done using the“dead-time” approach given above. This may be advantageous when thetransceiver has the capability of choosing alternate frequency bands forcommunicating. Estimates of interference in alternate bands provides thefoundation for an adaptive frequency hopped scheme.

[0256] It is understood that the examples and embodiments describedherein are for illustrative purposes only and that various modificationsor changes in light thereof will be suggested to persons skilled in theart and are to be included within the spirit and purview of thisapplication and scope of the appended claims and their full scope ofequivalents. For example, much of the above discussion concerns signalprocessing in the context of a wireless communication system wheremultiple inputs or multiple outputs are accessed by multiple transmitterantenna elements or multiple receiver antenna elements. However, thepresent invention is also useful in the context of wireline channelsaccessible via multiple inputs or multiple outputs.

What is claimed is:
 1. In a digital communication system, a method for communicating comprising the steps of: transmitting signals from one or more transmitter antenna elements; receiving said signals from via a plurality of receiver antenna elements; wherein separation of radiation patterns among either said transmitter antenna elements or said receiver antenna elements is insufficient to establish completely isolated spatial directions for communication; and wherein at least one of said transmitting and receiving steps comprises processing said signals to increase isolation between spatial directions employed for communication at a common frequency.
 2. The method of claim 1 wherein a channel coupling said plurality of transmitter antenna elements and receiver antenna elements at said common frequency is characterized by a spatial channel matrix having a rank greater than one.
 3. In a digital communication system, a method for communicating comprising the steps of: transmitting signals from one or more transmitter antenna elements; receiving said signals via a plurality of receiver antenna elements; wherein separation of radiation patterns among either said transmitter antenna elements or said receiver antenna elements is insufficient to establish completely isolated spatial directions for communication; and wherein at least one of said transmitting and receiving steps comprises processing said signals to increase isolation between subchannels, each subchannel associated with a spatial direction and a bin of a substantially orthogonalizing procedure.
 4. The method of claim 3 wherein said substantially orthogonalizing procedure belongs to a group including: an inverse Fast Fourier Transform, a Fast Fourier Transform, a Hilbert transform, a wavelet transform, and processing through a set of bandpass filter/frequency upconverter pairs operating at spaced apart frequencies.
 5. In a digital communication system, a method for preparing a sequence of symbols for transmission via a plurality of inputs of a channel: a) inputting said symbols of said sequence into a plurality of inputs corresponding to a plurality of subchannels of said channel, each subchannel corresponding to an input bin of a transmitter substantially orthogonalizing procedure and a spatial direction; b) for each input bin, spatially processing symbols inputted to said subchannels corresponding to said input bin, to develop a spatially processed symbol to assign to each combination of channel input and input bin of said transmitter substantially orthogonalizing procedure; and c) applying, independently for each said channel input, said transmitter substantially orthogonalizing procedure to said spatially processed symbols assigned to each said channel input.
 6. The method of claim 5 wherein said b) step has the effect of making spatial directions of said subchannels into a set of orthogonal spatial dimensions.
 7. The method of claim 5 wherein said transmitter substantially orthogonalizing procedure belongs to one of a group consisting of an inverse Fast Fourier Transform, a Fast Fourier Transform, a discrete cosine transform, a Hilbert transform, a wavelet transform, and processing through a plurality of bandpass filter/frequency converter pairs centered at spaced apart frequencies.
 8. The method of claim 5 further comprising the step of, after said c) step, applying a cyclic prefix processing procedure to a result of said substantially orthogonalizing procedure independently for each channel input.
 9. The method of claim 5 wherein said transmitter substantially orthogonalizing procedure is optimized to reduce interference to unintended receivers.
 10. The method of claim 5 wherein said b) step comprises, for each particular input bin,multiplying a vector comprising symbols allocated to subchannels corresponding to said input bin by a beneficial weighting matrix, elements of a result vector of said multiplying step corresponding to different channel inputs of said plurality of channel inputs.
 11. The method of claim 10 wherein said beneficial weighting matrix comprises an input singular matrix of a matrix containing values representing characteristics of said channel, said coupling said plurality of channel inputs to one or more channel outputs.
 12. The method of claim 10 wherein said beneficial weighting matrix is obtained from a matrix containing values representing characteristics of a channel coupling said plurality of channel inputs to one or more channel outputs.
 13. The method of claim 10 wherein said beneficial weighting matrix is chosen to reduce interference to unintended receivers.
 14. The method of claim 13 wherein said beneficial weighting matrix is chosen based upon characterization of a desired signal subspace.
 15. The method of claim 14 wherein said beneficial weighting matrix is chosen further based upon characterization of an undesired signal subspace.
 16. The method of claim 15 wherein characterizations of said desired signal subspace and said undesired signal subspace are averaged over at least one of time and frequency.
 17. The method of claim 10 wherein said b) step comprises performing said spatial processing step so as to reduce interference radiated to unintended receivers.
 18. The method of claim 10 wherein said b) step comprises, for each input bin, allocating symbols to each combination of channel input and input bin so that there is a one-to-one mapping between spatial direction of a particular subchannel to which a particular symbol has been allocated and channel input to which said particular symbol is allocated.
 19. The method of claim 10 further comprising the step of prior to said b) step applying a coding procedure to said symbols.
 20. The method of claim 19 wherein said coding procedure is applied independently for each of said subchannels.
 21. The method of claim 19 wherein said coding procedure is applied independently for each group of subchannels corresponding to an input bin of said substantially orthogonalizing procedure.
 22. The method of claim 19 wherein said coding procedure is applied independently for each group of subchannels corresponding to a particular spatial direction.
 23. The method of claim 19 wherein said coding procedure is applied integrally across all of said subchannels.
 24. The method of claim 19 wherein said coding procedure belongs to a group consisting of: convolutional coding, Reed-Solomon coding, CRC coding, block coding, trellis coding, turbo coding, and interleaving.
 25. The method of claim 19 wherein said coding procedure comprises a trellis coding procedure.
 26. The method of claim 25 wherein a code design of said trellis coding procedure is based on one of: improved bit error performance in interference channels, a periodic product distance metric, exhaustive code polynomial search for favorable bit error rate polynomial searches, combined weighting of product distance and Euclidean distance, product distance of multiple Euclidean distances over short code segments or over a multi-dimensional symbol, and sum of product distances over short code segments.
 27. The method of claim 25 wherein a code design of said trellis coding procedure is optimized for performance in a fading matrix channel.
 28. The method of claim 19 wherein said coding procedure comprises a one-dimensional trellis coding procedure followed by an interleaving procedure with sequential groups of symbols output by said trellis coding having their internal order maintained by said interleaving procedure.
 29. The method of claim 19 wherein said coding procedure comprises a multi-dimensional trellis coding procedure followed by an interleaving procedure with groups of one-dimensional symbols output simultaneously by said multi-dimensional trellis coding procedure having their internal order maintained by said interleaving procedure.
 30. The method of claim 10 wherein bit loading and power are allocated to each subchannel.
 31. The method of claim 10 further comprising the step of retransmitting symbols by repeating at least one of said a), b), and c) steps upon receipt of a notification that said symbols to be retransmitted have been incorrectly received.
 32. The method of claim 10 wherein said channel comprises a wireless channel and said plurality of channel inputs are associated with a corresponding plurality of transmitter antenna elements
 33. The method of claim 32 wherein said plurality of transmitter antenna elements are co-located.
 34. The method of claim 32 wherein said plurality of transmitters are at disparate locations.
 35. A method of processing a sequence of symbols received via a plurality of outputs of a channel, said method comprising the steps of: a) applying a receiver substantially orthogonalizing procedure to said sequence of symbols, said procedure being applied independently for each of said plurality of channel outputs, each output symbol of said receiver substantially orthogonalizing procedure corresponding to a particular output bin and a particular one of said channel outputs; and b) for each output bin, spatially processing symbols corresponding to said output bin to develop spatially processed symbols assigned to a plurality of spatial directions, each combination of spatial direction and output bin specifying one of a plurality of subchannels.
 36. The method of claim 35 wherein said b) step has the effect of making said plurality of spatial directions into a set of orthogonal spatial dimensions.
 37. The method of claim 35 wherein said receiver substantially orthogonalizing procedure belongs to one of a group consisting of an inverse Fast Fourier Transform, a Fast Fourier Transform, a discrete cosine transform, a Hilbert transform, a wavelet transform, and processing through a plurality of bandpass filter/frequency converter pairs centered at spaced apart frequencies.
 38. The method of claim 35 further comprising the step of, prior to said a) step, applying a cyclic prefix removal procedure to said sequence of symbols independently for each of said channel outputs.
 39. The method of claim 35 wherein said receiver substantially orthogonalizing procedure is optimized to reduce deleterious effects of interference from undesired co-channel transmitters.
 40. The method of claim 35 wherein said b) step comprises, for each particular output bin, multiplying a vector comprising symbols of said output bin by a beneficial weighting matrix, elements of a result vector of said multiplying step corresponding to different spatial directions.
 41. The method of claim 40 wherein said beneficial weighting matrix comprises an output singular vector of a matrix containing values representing characteristics of said channel, said channel coupling one or more channel inputs to said plurality of channel outputs.
 42. The method of claim 40 wherein said beneficial weighting matrix is chosen to minimize deleterious effects of interference from undesired transmitters.
 43. The method of claim 42 wherein said beneficial weighting matrix is chosen based upon characterization of a desired signal subspace.
 44. The method of claim 43 wherein said beneficial weighting matrix is chosen further based upon characterization of an undesired signal subspace.
 45. The method of claim 44 wherein said characterizations of said desired signal subspace and said undesired signal subspace are averaged over at least one of time and frequency.
 46. The method of claim 40 wherein said beneficial weighting matrix is obtained from a matrix containing values representing characteristics of said channel, said channel coupling one or more channel inputs and said plurality of channel outputs.
 47. The method of claim 46 wherein said beneficial weighting matrix is obtained by an MMSE procedure.
 48. The method of claim 35 further comprising the step of after said b) step applying a decoding procedure to said symbols.
 49. The method of claim 48 wherein said decoding procedure is applied independently for each of said plurality of subchannels.
 50. The method of claim 48 wherein said decoding procedure is applied independently for each group of subchannels corresponding to an output bin of said substantially orthogonalizing procedure.
 51. The method of claim 48 wherein said decoding procedure is applied independently for each group of subchannels corresponding to a spatial direction.
 52. The method of claim 48 wherein said decoding procedure is applied integrally across all of said plurality of subchannels.
 53. The method of claim 48 wherein said decoding procedure belongs to a group consisting of: Reed-Solomon decoding, CRC decoding, block decoding, and de-interleaving.
 54. The method of claim 48 wherein said decoding procedure comprises a code sequence detection procedure to decode a trellis code, or convolutional code.
 55. The method of claim 54 wherein said code sequence detection procedure employs a metric belonging to a group consisting of: Euclidean metric, weighted Euclidean metric, and Hamming metric.
 56. The method of claim 48 wherein said decoding procedure reduces deleterious effects of interference from undesired transmitters.
 57. The method of claim 35 further comprising the step of: sending a retransmission request when received symbols are determined to include errors.
 58. The method of claim 35 wherein said channel comprises a wireless channel and said plurality of channel outputs are coupled to a plurality of corresponding receiver antenna elements.
 59. The method of claim 35 wherein said plurality of receiver antenna elements are co-located.
 60. The method of claim 35 wherein said plurality of receiver antenna elements are at disparate locations.
 61. In a digital communication system, a method for preparing a sequence of symbols for transmission via a plurality of inputs to a channel, said method comprising the steps of: selecting a weighting vector for optimal transmission; applying a transmitter substantially orthogonalizing procedure to said sequence of symbols to develop a time domain symbol sequence; and multiplying at least one symbol of said time domain symbol sequence by said weighting vector to develop a result vector, elements of said result vector corresponding to symbols to be transmitted via individual ones of said plurality of channel inputs.
 62. The method of claim 61 wherein said weighting vector comprises an element indicating delay to be applied for a particular one of said plurality of channel inputs.
 63. The method of claim 61 wherein said weighting vector is optimized to reduce interference to unintended receivers.
 64. The method of claim 61 wherein said weighting vector is chosen based upon characterization of a desired signal subspace.
 65. The method of claim 64 wherein said weighting vector is chosen further based upon characterization of an undesired signal subspace.
 66. The method of claim 65 wherein said characterizations of said desired signal subspace and said undesired signal subspace are averaged over at least one of time and frequency.
 67. The method of claim 61 wherein said channel comprises a wireless channel and said plurality of channel inputs are associated with a plurality of transmitter antenna elements.
 68. In a digital communication system, a method for processing a plurality of symbols received via a plurality of outputs of a channel, said method comprising the steps of: selecting a weighting vector for optimal reception; multiplying an input vector whose elements correspond to symbols received substantially simultaneously via a selected one of said plurality of channel outputs by said weighting vector to obtain a time domain symbol corresponding to a particular input bin of a receiver substantially orthogonalizing procedure; repeating said multiplying step for successive received symbols to obtain time domain symbols corresponding to successive input bins of said receiver substantially orthogonalizing procedure; and applying said receiver substantially orthogonalizing procedure to said obtained time domain symbols.
 69. The method of claim 68 wherein said weighting vector comprises an element indicating delay to be applied for a particular one of said plurality of channel outputs.
 70. The method of claim 68 wherein said weighting vector is optimized to reduce deleterious effects of interference from unintended transmitters.
 71. The method of claim 68 wherein said weighting vector is chosen based upon characterization of a desired signal subspace.
 72. The method of claim 71 wherein said weighting vector is chosen further based upon characterization of an undesired signal subspace.
 73. The method of claim 72 wherein said characerizations of said desired signal subspace and said undesired signal subspace are averaged over at least one of frequency and time.
 74. The method of claim 71 wherein said channel comprises a wireless channel and said plurality of channel outputs are associated with a plurality of corresponding receiver antenna elements.
 75. In a digital communication system, a method of preparing symbols for transmission via a plurality of inputs of a channel, said method comprising the steps of: directing symbols to input bins of a transmitter substantially orthogonalizing procedure so that each input bin has an allocated symbol; for each particular input bin, spatially processing said symbol allocated to said particular input bin to develop a spatially processed symbol vector, each element of said spatially processed symbol vector being assigned to one of said channel inputs; applying said transmitter substantially orthogonalizing procedure for a particular channel input, inputs to said substantially orthogonalizing procedure being for each input bin, a symbol of said processed symbol vector for said input bin corresponding to said particular channel input; and repeating said applying step for each of said plurality of channel inputs.
 76. The method of claim 75 further comprising the step of: applying a cyclic prefix processing procedure to outputs of said substantially orthogonalizing procedure independently for each particular channel input.
 77. The method of claim 75 wherein said transmitter substantially orthogonalizing procedure is optimized to reduce interference to unintended receivers.
 78. The method of claim 75 wherein said processing step comprises: multiplying said symbol allocated to said particular input bin by a beneficial weighting vector to obtain said spatially processed symbol vector.
 79. The method of claim 78 wherein said beneficial weighting vector is an input singular vector of a matrix storing values indicative of said channel, said channel coupling said plurality of channel inputs and one or more channel outputs.
 80. The method of claim 78 wherein said beneficial weighting vector is chosen to select a beneficial spatial direction for transmission.
 81. The method of claim 80 wherein said beneficial weighting vector is chosen to reduce interference to unintended receivers.
 82. The method of claim 81 wherein said beneficial weighting vector is chosen based upon characterization of a desired signal subspace
 83. The method of claim 82 wherein said beneficial weighting vector is chosen further based upon characterization of an undesired signal subspace.
 84. The method of claim 83 wherein said characterizations of said desired signal subspace and said undesired signal subspace are averaged over at least one of time and frequency.
 85. The method of claim 75 wherein said channel comprises a wireless channel and said plurality of channel inputs are associated with a corresponding plurality of transmitter antenna elements.
 86. In a digital communication system, a method for processing symbols received by a plurality of outputs of a channel comprising the step of: applying a receiver substantially orthogonalizing procedure to symbols received via a particular one of said channel outputs; repeating said applying step for each of said channel outputs to develop a result vector for each of a plurality of output bins of said receiver substantially orthogonalizing procedure, said result vector including a result symbol for each of said channel outputs; and for each particular output bin of said receiver substantially orthogonalizing procedure, spatially processing said result vector for said particular output bin to develop a spatially processed result symbol for said particular output bin.
 87. The method of claim 86 further comprising the step of: prior to said applying step, applying a cyclic prefix removal procedure to symbols independently for each of said channel outputs.
 88. The method of claim 86 wherein said substantially orthogonalizing procedure is optimized to reduce deleterious effects of interference from unintended transmitters.
 89. The method of claim 86 wherein said spatially processing step comprises multiplying a beneficial weighting vector by said result vector to obtain said spatially processed result symbol.
 90. The method of claim 88 wherein said beneficial weighting vector is an input singular vector of a matrix storing values indicative of characteristics of said channel, said channel coupling one or more chanel inputs and said plurality of channel outputs.
 91. The method of claim 88 wherein said beneficial weighting vector is chosen to select a particular spatial direction for reception.
 92. The method of claim 91 wherein said beneficial weighting vector is chosen to minimize deleterious effects of interference from unintended transmitters.
 93. The method of claim 91 wherein said beneficial weighting vector is chosen based upon characterization of a desired signal subspace.
 94. The method of claim 93 wherein said beneficial weighting vector is chosen based upon characterization of an undesired signal subspace.
 95. The method of claim 94 wherein said characterizations of said desired signal subspace and said undesired signal subspace are averaged over at least one of time and frequency.
 96. The method of claim 86 wherein said channel comprises a wireless channel and said plurality of channel outputs are associated with a corresponding plurality of channel outputs.
 97. In a digital communication system including a communication channel having one or more inputs and at least one or more outputs, a method for determining characteristics of said channel based on signals received by said one or more outputs, comprising the steps of: a) receiving via said one or more channel outputs, at least ν training symbols transmitted via a particular spatial direction of said channel, ν being an extent in symbol periods of a duration of significant terms of an impulse response of a channel; and b) applying a substantially orthogonalizing procedure to said received at least ν training symbols to obtain a time domain response for said spatial direction; and c) applying an inverse of said substantially orthogonalizing procedure to a zero-padded version of said time domain response to obtain a frequency response for said particular spatial direction.
 98. The method of claim 97 wherein said substantially orthogonalizing procedure comprises an inverse Fast Fourier Transform and said inverse of said substantially orthogonalizing procedure comprises a Fast Fourier Transform.
 99. The method of claim 98 wherein said a) step comprises receiving exactly ν training symbols.
 100. The method of claim 97 further comprising the step of repeating said a), b), c), and d) steps for a plurality of spatial directions.
 101. The method of claim 99 wherein each of said plurality of spatial directions corresponds to transmission through one of said plurality of channel inputs exclusively.
 102. The method of claim 98 wherein said ν training symbols belong to a burst of N symbols and said characteristics are determined for said burst.
 103. The method of claim 102 further comprising the steps of repeating said a), b), c), and d) steps for successive bursts.
 104. The method of claim 103 further comprising the step of after, said b) step, smoothing said time-domain response over successive bursts.
 105. The method of claim 104 wherein said smoothing step comprises Kalman filtering.
 106. The method of claim 104 wherein said smoothing step comprises Wiener filtering.
 107. The method of claim 97 wherein said communication channel comprises known and unknown components, wherein said effects of said known components are removed by deconvolution, and characteristics of said unknown components are determined by said a), b), c), and d) steps, thereby reducing.
 108. In a digital communication system including a communication channel having one or more inputs and one or more outputs, a method for determining characteristics of said channel based on signals received via one or more channel outputs, comprising the steps of: receiving training symbols via said channel outputs; and computing characteristics of said channel based on said received training symbols and assumptions that an impulse response of said channel is substantially time-limited and that variation of said impulse response over time is continuous.
 109. In a digital communication system, a method for communicating over a channel having at least one input and at least one output, and having a plurality of either inputs or outputs, said method comprising the steps of: dividing said channel into a plurality of subchannels, each subchannel corresponding to a combination of spatial direction and an input bin of a substantially orthogonalizing procedure; and communicating symbols over one or more of said plurality of subchannels.
 110. In a digital communication system, a method for preparing a sequence of symbols for transmission via a plurality of inputs of a channel, comprising the steps of: a) inputting said symbols of said sequence into a plurality of input corresponding to a plurality of subchannels of said channel, each subchannel corresponding to an input bin of a transmitter substantially orthogonalizing procedure and a channel input; and b) applying, independently for each said channel input, said transmitter substantially orthogonalizing procedure to said symbols assigned to each said channel input.
 111. A method of processing a sequence of symbols received via a plurality of outputs of a channel, said method comprising the steps of: a) applying a substantially orthogonalizing procedure to said sequence of symbols, said procedure being applied independently for each of said plurality of channel outputs, each output symbol of said substantially orthogonalizing procedure corresponding to a subchannel identified by a combination of a particular output bin and a particular one of said channel outputs; and b) processing symbols in said subchannels.
 112. In a digital communication system, apparatus for communicating comprising: a transmitter that transmits signals from one or more transmitter antenna elements; a receiver that receives said signals from via a plurality of receiver antenna elements; wherein separation of radiation patterns among either said transmitter antenna elements or said receiver antenna elements is insufficient to establish completely isolated spatial directions for communication; and wherein at least one of said transmitter and said receiver comprises a processor that processes said signals to increase isolation between spatial directions employed for communication at a common frequency.
 113. The apparatus of claim 112 wherein a channel coupling said plurality of transmitter antenna elements and receiver antenna elements at said common frequency is characterized by a spatial channel matrix having a rank greater than one.
 114. In a digital communication system, apparatus for communicating comprising: a transmitter transmitting signals from one or more transmitter antenna elements; a receiver receiving said signals via a plurality of receiver antenna elements; wherein separation of radiation patterns among either said transmitter antenna elements or said receiver antenna elements is insufficient to establish completely isolated spatial directions for communication; and wherein at least one of said transmitter and said receiver comprises a processor that processes said signals to increase isolation between subchannels, each subchannel associated with a spatial direction and a bin of a substantially orthogonalizing procedure.
 115. The apparatus of claim 114 wherein said substantially orthogonalizing procedure belongs to a group including: an inverse Fast Fourier Transform, a Fast Fourier Transform, a Hilbert transform, a wavelet transform, and processing through a set of bandpass filter/frequency upconverter pairs operating at spaced apart frequencies.
 116. In a digital communication system, apparatus for preparing a sequence of symbols for transmission via a plurality of inputs of a channel: a plurality of parallel subchannel inputs receiving said symbols, said parallel subchannel inputs corresponding to a plurality of subchannels, each subchannel corresponding to an input bin of a transmitter substantially orthogonalizing procedure and a spatial direction; a spatial processor that, for each input bin, spatially processor symbols received by said subchannel inputs corresponding to said input bin, to develop a spatially processed symbol to assign to each combination of channel input and input bin of said transmitter substantially orthogonalizing procedure; and a substantially orthogonal procedure processor system that applies, independently for each said channel input, said transmitter substantially orthogonalizing procedure to said spatially processed symbols assigned to each said channel input.
 117. The apparatus of claim 116 wherein said spatial processor has the effect of making spatial directions of said subchannels into a set of orthogonal spatial dimensions.
 118. The apparatus of claim 116 wherein said transmitter substantially orthogonalizing procedure belongs to one of a group consisting of an inverse Fast Fourier Transform, a Fast Fourier Transform, a discrete cosine transform, a Hilbert transform, a wavelet transform, and processing through a plurality of bandpass filter/frequency converter pairs centered at spaced apart frequencies.
 119. The apparatus of claim 116 further comprising: a cyclic prefix processor that applies a cyclic prefix processing procedure to a result of said substantially orthogonalizing procedure independently for each channel input.
 120. The apparatus of claim 116 wherein said transmitter substantially orthogonalizing procedure is optimized to reduce interference to unintended receivers.
 121. The apparatus of claim 116 wherein said spatial processor comprises, for each particular input bin, a weight multiplier that multiplies a vector comprising symbols allocated to subchannels corresponding to said input bin by a beneficial weighting matrix, elements of a result vector of said weight multiplier corresponding to different channel inputs of said plurality of channel inputs.
 122. The apparatus of claim 121 wherein said beneficial weighting matrix comprises an input singular matrix of a matrix containing values representing characteristics of said channel, said channel coupling said plurality of channel inputs to one or more channel outputs.
 123. The apparatus of claim 121 wherein said beneficial weighting matrix is obtained from a matrix containing values representing characteristics of a channel coupling said plurality of channel inputs to one or more channel outputs.
 124. The apparatus of claim 121 wherein said beneficial weighting matrix is chosen to reduce interference to unintended receivers.
 125. The apparatus of claim 124 wherein said beneficial weighting matrix is chosen based upon characterization of a desired signal subspace.
 126. The apparatus of claim 125 wherein said beneficial weighting matrix is chosen further based upon characterization of an undesired signal subspace.
 127. The apparatus of claim 126 wherein characterizations of said desired signal subspace and said undesired signal subspace are averaged over at least one of time and frequency.
 128. The apparatus of claim 116 wherein said spatial processor operates so as to reduce interference radiated to unintended receivers.
 129. The apparatus of claim 116 wherein said spatial processor, allocates symbols to each combination of channel input and input bin so that there is a one-to-one mapping between spatial direction of a particular subchannel to which a particular symbol has been allocated and channel input to which said particular symbol is allocated.
 130. The apparatus of claim 116 further comprising a coder that applies a coding procedure to said symbols prior to processing by said spatial processor.
 131. The apparatus of claim 130 wherein said coding procedure is applied independently for each of said subchannels.
 132. The apparatus of claim 130 wherein said coding procedure is applied independently for each group of subchannels corresponding to an input bin of said substantially orthogonalizing procedure.
 133. The apparatus of claim 130 wherein said coding procedure is applied independently for each group of subchannels corresponding to a particular spatial direction.
 134. The apparatus of claim 130 wherein said coding procedure is applied integrally across all of said subchannels.
 135. The apparatus of claim 130 wherein said coding procedure belongs to a group consisting of: convolutional coding, Reed-Solomon coding, CRC coding, block coding, trellis coding, turbo coding, and interleaving.
 136. The apparatus of claim 130 wherein said coding procedure comprises a trellis coding procedure.
 137. The apparatus of claim 136 wherein a code design of said trellis coding procedure is based on one of: improved bit error performance in interference channels, a periodic product distance metric, exhaustive code polynomial search for favorable bit error rate polynomial searches, combined weighting of product distance and Euclidean distance, product distance of multiple Euclidean distances over short code segments or over a multi-dimensional symbol, and sum of product distances over short code segments.
 138. The apparatus of claim 136 wherein a code design of said trellis coding procedure is optimized for performance in a fading matrix channel.
 139. The apparatus of claim 130 wherein said coding procedure comprises a one-dimensional trellis coding procedure followed by an interleaving procedure with sequential groups of symbols output by said trellis coding having their internal order maintained by said interleaving procedure.
 140. The apparatus of claim 130 wherein said coding procedure comprises a multi-dimensional trellis coding procedure followed by an interleaving procedure with groups of one-dimensional symbols output simultaneously by said multi-dimensional trellis coding procedure having their internal order maintained by said interleaving procedure.
 141. The apparatus of claim 130 wherein bit loading and power are allocated to each subchannel.
 142. The apparatus of claim 116 further comprising an ARQ system that retransmits symbols via at least one of said spatial processor, and said substantially orthogonalizing procedure processor upon receipt of a notification that said symbols to be retransmitted have been incorrectly received.
 143. The apparatus of claim 116 wherein said channel comprises a wireless channel and said plurality of channel inputs are associated with a corresponding plurality of transmitter antenna elements
 144. The apparatus of claim 142 wherein said plurality of transmitter antenna elements are co-located.
 145. The apparatus of claim 144 wherein said plurality of transmitters are at disparate locations.
 146. Apparatus of processing a sequence of symbols received via a plurality of outputs of a channel, said apparatus comprising: a substantially orthogonalizing procedure processor system that applies a receiver substantially orthogonalizing procedure to said sequence of symbols, said procedure being applied independently for each of said plurality of channel outputs, each output symbol of said substantially orthogonalizing procedure corresponding to a particular output bin and a particular one of said channel outputs; and a spatial processor that, for each output bin, spatially processes symbols corresponding to said output bin to develop spatially processed symbols assigned to a plurality of spatial directions, each combination of spatial direction and output bin specifying one of a plurality of subchannels.
 147. The apparatus of claim 146 wherein said spatial processor operates to make said plurality of spatial directions into a set of orthogonal spatial dimensions.
 148. The apparatus of claim 146 wherein said receiver substantially orthogonalizing procedure belongs to one of a group consisting of an inverse Fast Fourier Transform, a Fast Fourier Transform, a discrete cosine transform, a Hilbert transform, a wavelet transform, and processing through a plurality of bandpass filter/frequency converter pairs centered at spaced apart frequencies.
 149. The apparatus of claim 146 further comprising: a cyclic prefix processor that applies a cyclic prefix removal procedure to said sequence of symbols independently for each of said channel outputs.
 150. The apparatus of claim 146 wherein said receiver substantially orthogonalizing procedure is optimized to reduce deleterious effects of interference from undesired co-channel transmitters.
 151. The apparatus of claim 146 wherein said spatial processor comprises, for each particular output bin, a weight multiplier that multiplies a vector comprising symbols of said output bin by a beneficial weighting matrix, elements of a result vector of said multiplier corresponding to different spatial directions.
 152. The apparatus of claim 151 wherein said beneficial weighting matrix comprises an output singular vector of a matrix containing values representing characteristics of said channel, said channel coupling one or more channel inputs to said plurality of channel outputs.
 153. The apparatus of claim 151 wherein said beneficial weighting matrix is chosen to minimize deleterious effects of interference from undesired transmitters.
 154. The apparatus of claim 151 wherein said beneficial weighting matrix is chosen based upon characterization of a desired signal subspace.
 155. The apparatus of claim 154 wherein said beneficial weighting matrix is chosen further based upon characterization of an undesired signal subspace.
 156. The apparatus of claim 155 wherein said characterizations of said desired signal subspace and said undesired signal subspace are averaged over at least one of time and frequency.
 157. The apparatus of claim 151 wherein said beneficial weighting matrix is obtained from a matrix containing values representing characteristics of said channel, said channel coupling one or more channel inputs and said plurality of channel outputs.
 158. The apparatus of claim 157 wherein said beneficial weighting matrix is obtained by an MMSE procedure.
 159. The apparatus of claim 146 further comprising: a decoder that applies a decoding procedure to said spatially processed symbols.
 160. The apparatus of claim 159 wherein said decoding procedure is applied independently for each of said plurality of subchannels.
 161. The apparatus of claim 159 wherein said decoding procedure is applied independently for each group of subchannels corresponding to an output bin of said substantially orthogonalizing procedure.
 162. The apparatus of claim 159 wherein said decoding procedure is applied independently for each group of subchannels corresponding to a spatial direction.
 163. The apparatus of claim 159 wherein said decoding procedure is applied integrally across all of said plurality of subchannels.
 164. The apparatus of claim 159 wherein said decoding procedure belongs to a group consisting of: Reed-Solomon decoding, CRC decoding, block decoding, and de-interleaving.
 165. The apparatus of claim 159 wherein said decoding procedure comprises a code sequence detection procedure to decode a trellis code, or convolutional code.
 166. The apparatus of claim 165 wherein said code sequence detection procedure employs a metric belonging to a group consisting of: Euclidean metric, weighted Euclidean metric, and Hamming metric.
 167. The apparatus of claim 159 wherein said decoding procedure reduces deleterious effects of interference from undesired transmitters.
 168. The apparatus of claim 146 further comprising: a system that sends a retransmission request when received symbols are determined to include errors.
 169. The apparatus of claim 170 wherein said channel comprises a wireless channel and said plurality of channel outputs are coupled to a plurality of corresponding receiver antenna elements.
 171. The apparatus of claim 170 wherein said plurality of receiver antenna elements are co-located.
 172. The apparatus of claim 170 wherein said plurality of receiver antenna elements are at disparate locations.
 173. In a digital communication system, apparatus for preparing a sequence of symbols for transmission via a plurality of inputs to a channel, said apparatus comprising: a substantially orthogonal procedure processor that applies a transmitter substantially orthogonalizing procedure to said sequence of symbols to develop a time domain symbol sequence; and a weight multiplier that multiplies at least one symbol of said time domain symbol sequence by a weighting vector selected for improved communication to develop a result vector, elements of said result vector corresponding to symbols to be transmitted via individual ones of said plurality of channel inputs.
 174. The apparatus of claim 173 wherein said weighting vector comprises an element indicating delay to be applied for a particular one of said plurality of channel inputs.
 175. The apparatus of claim 174 wherein said weighting vector is optimized to reduce interference to unintended receivers.
 176. The apparatus of claim 173 wherein said weighting vector is chosen based upon characterization of a desired signal subspace.
 177. The apparatus of claim 176 wherein said weighting vector is chosen further based upon characterization of an undesired signal subspace.
 178. The apparatus of claim 177 wherein said characterizations of said desired signal subspace and said undesired signal subspace are averaged over at least one of time and frequency.
 179. The apparatus of claim 173 wherein said channel comprises a wireless channel and said plurality of channel inputs are associated with a plurality of transmitter antenna elements.
 180. 180. In a digital communication system, apparatus for processing a plurality of symbols received via a plurality of outputs of a channel, said apparatus comprising: a weight multiplier that performs a multiplication of an input vector whose elements correspond to symbols received substantially simultaneously via a selected one of said plurality of channel outputs by a weighting vector to obtain a time domain symbol corresponding to a particular input bin of a receiver substantially orthogonalizing procedure and that repeats said multiplication for successive received symbols to obtain time domain symbols corresponding to successive input bins of said receiver substantially orthogonalizing procedure; and a substantial orthogonalizing procedure processor that applies said substantially orthogonalizing procedure processor to said obtained time domain symbols.
 181. The apparatus of claim 180 wherein said weighting vector comprises an element indicating delay to be applied for a particular one of said plurality of channel outputs.
 182. The apparatus of claim 180 wherein said weighting vector is optimized to reduce deleterious effects of interference from unintended transmitters.
 183. The apparatus of claim 180 wherein said weighting vector is chosen based upon characterization of a desired signal subspace.
 184. The apparatus of claim 183 wherein said weighting vector is chosen further based upon characterization of an undesired signal subspace.
 185. The apparatus of claim 184 wherein said characterizations of said desired signal subspace and said undesired signal subspace are averaged over at least one of frequency and time.
 186. The apparatus of claim 180 wherein said channel comprises a wireless channel and said plurality of channel outputs are associated with a plurality of corresponding receiver antenna elements.
 187. In a digital communication system, apparatus for preparing symbols for transmission via a plurality of inputs of a channel, said apparatus comprising: a plurality of symbol inputs, each of said symbol inputs receiving a symbol intended for a particular input bin of a transmitter substantially orthogonalizing procedure so that each of a plurality of input bins of said transmitter substantially orthongonalizing procedure has an allocated symbol; a spatial processor that, for each particular input bin of said plurality of input bins, spatially processes said symbol allocated to said particular input bin to develop a spatially processed symbol vector, each element of said spatially processed symbol vector being assigned to one of said channel inputs; and a substantially orthogonalizing procedure processor that applies said substantially orthogonalizing procedure for a particular channel input, inputs to said substantially orthogonalizing procedure being for each input bin, a symbol of said processed symbol vector for said input bin corresponding to said particular channel input, and that applies said sustantially orthogonalizing procedure for each of said plurality of channel inputs.
 188. The apparatus of claim 187 further comprising: a cyclic prefix processor that applies a cyclic prefix processing procedure to outputs of said substantially orthogonalizing procedure independently for each particular channel input.
 189. The apparatus of claim 187 wherein said substantially orthogonalizing procedure is optimized to reduce interference to unintended receivers.
 190. The apparatus of claim 187 wherein said spatial processor comprises: a weight multiplier that multiplies said symbol allocated to said particular input bin by a beneficial weighting vector to obtain said spatially processed symbol vector.
 191. The apparatus of claim 190 wherein said beneficial weighting vector is an input singular vector of a matrix storing values indicative of characteristics of said channel, said channel coupling said plurality of channel inputs and one or more channel outputs.
 192. The apparatus of claim 190 wherein said beneficial weighting vector is chosen to select a beneficial spatial direction for transmission.
 193. The apparatus of claim 191 wherein said beneficial weighting vector is chosen to reduce interference to unintended receivers.
 194. The apparatus of claim 193 wherein said beneficial weighting vector is chosen based upon characterization of a desired signal subspace
 195. The apparatus of claim 194 wherein said beneficial weighting vector is chosen further based upon characterization of an undesired signal subspace.
 196. The apparatus of claim 195 wherein said characterizations of said desired signal subspace and said undesired signal subspace are averaged over at least one of time and frequency.
 197. The apparatus of claim 187 wherein said channel comprises a wireless channel and said plurality of channel inputs are associated with a corresponding plurality of transmitter antenna elements.
 198. In a digital communication system, apparatus for processing symbols received by a plurality of outputs of a channel comprising: a substantially orthogonalizing procedure processor that applies a receiver substantially orthogonalizing procedure to symbols received via a particular one of said channel outputs and that said applies said receiver substantially orthogonalizing procedure for each of said channel outputs to develop a result vector for each of a plurality of output bins of said substantially orthogonalizing procedure, said result vector including a result symbol for each of said channel outputs; and a spatial processor that, for each particular output bin of said substantially orthogonalizing procedure, spatially processes said result vector for said particular output bin to develop a spatially processed result symbol for said particular output bin.
 199. The apparatus of claim 198 further comprising: a cyclic prefix removal processor that applies a cyclic prefix removal procedure to symbols independently for each of said channel outputs.
 200. The apparatus of claim 198 wherein said substantially orthogonalizing procedure is optimized to reduce deleterious effects of interference from unintended transmitters.
 201. The apparatus of claim 198 wherein said spatially processor comprises a weight multiplier that multiplies a beneficial weighting vector by said result vector to obtain said spatially processed result symbol.
 202. The apparatus of claim 201 wherein said beneficial weighting vector is an input singular vector of a matrix storing values indicative of characteristics of said channel, said channel coupling one or more chanel inputs and said plurality of channel outputs.
 203. The apparatus of claim 201 wherein said beneficial weighting vector is chosen to select a particular spatial direction for reception.
 204. The apparatus of claim 203 wherein said beneficial weighting vector is chosen to minimize deleterious effects of interference from unintended transmitters.
 205. The apparatus of claim 204 wherein said beneficial weighting vector is chosen based upon characterization of a desired signal subspace.
 206. The apparatus of claim 205 wherein said beneficial weighting vector is chosen based upon characterization of an undesired signal subspace.
 207. The apparatus of claim 206 wherein said characterizations of said desired signal subspace and said undesired signal subspace are averaged over at least one of time and frequency.
 208. The apparatus of claim 198 wherein said channel comprises a wireless channel and said plurality of channel outputs are associated with a corresponding plurality of channel outputs.
 209. In a digital communication system including a communication channel having one or more inputs and at least one or more outputs apparatus for determining characteristics of said channel based on signals received by said one or more outputs, comprising: a receiver system receiving via said one or more channel outputs, at least training symbols transmitted via a particular spatial direction of said channel, being an extent in symbol periods of a duration of significant terms of an impulse response of a channel; a substantially orthogonalizing procedure processor that applies a substantially orthogonalizing procedure processor to said received at least training symbols to obtain a time domain response for said particular spatial direction; and an inverse substantially orthogonalizing procedure processor that applies an inverse of said substantially orthogonalizing procedure to a zero-padded version of said time domain response to obtain a frequency response for said particular spatial direction.
 210. The apparatus of claim 209 wherein said substantially orthogonalizing procedure comprises an inverse Fast Fourier Transform and said inverse of said substantially orthogonalizing procedure comprises a Fast Fourier Transform.
 211. The apparatus of claim 209 wherein said receiver system receives exactly training symbols.
 212. The apparatus of claim 209 wherein said receiver system, said substantially orthogonalizing procedure processor and said inverse substantially orthogonalizing procedure process operate repeatedly for a plurality of spatial directions.
 213. The apparatus of claim 209 wherein each of said plurality of spatial directions corresponds to transmission through one of said plurality of channel inputs exclusively.
 214. The apparatus of claim 209 wherein said training symbols belong to a burst of N symbols and said characteristics are determined for said burst.
 215. The apparatus of claim 214 said receiver system, said substantially orthogonalizing procedure processor and said inverse substantially orthogonalizing procedure process operate repeatedly for a plurality of bursts.
 216. The apparatus of claim 215 further comprising: means for smoothing said time-domain response over successive bursts.
 217. The apparatus of claim 216 wherein said smoothing means comprises: means for Kalman filtering said time-domain response over successive bursts.
 218. The apparatus of claim 217 wherein said smoothing means comprises means for Wiener filtering said time-domain response over successive bursts.
 219. The apparatus of claim 209 wherein said communication channel comprises known and unknown components, wherein said effects of said known components are removed by deconvolution, and characteristics of said unknown components are determined by said a), b), c), and d) steps, thereby reducing.
 220. In a digital communication system including a communication channel having one or more inputs and one or more outputs, apparatus for determining characteristics of said channel based on signals received via one or more channel outputs, comprising: a receiver that receives training symbols via said channel outputs; and a processor that computes characteristics of said channel based on said received training symbols and assumptions that an impulse response of said channel is substantially time-limited and that variation of said impulse response over time is continuous.
 221. In a digital communication system, apparatus for communicating over a channel having at least one input and at least one output, and having a plurality of either inputs or outputs, said apparatus comprising: means for dividing said channel into a plurality of subchannels, each subchannel corresponding to a combination of spatial direction and an input bin of a substantially orthogonalizing procedure; and means for communicating symbols over one or more of said plurality of subchannels.
 222. In a digital communication system, apparatus for preparing a sequence of symbols for transmission via a plurality of inputs of a channel, said apparatus comprising: a plurality of parallel subchannel inputs that receive said sequence of symbols, said subchannel inputs corresponding to a plurality of subchannels, each subchannel corresponding to an input bin of a transmitter substantially orthogonalizing procedure and a channel input; and a substantially orthogonalizing procedure processor that applies, independently for each said channel input, said transmitter substantially orthogonalizing procedure to said symbols assigned to each said channel input.
 223. Apparatus for processing a sequence of symbols received via a plurality of outputs of a channel, said apparatus comprising the steps of: a substantially orthogonalizing procedure processor that applies a receiver substantially orthogonalizing procedure to said sequence of symbols, said procedure being applied independently for each of said plurality of channel outputs, each output symbol of said receiver substantially orthogonalizing procedure corresponding to a subchannel identified by a combination of a particular output bin and a particular one of said channel outputs; and a processor that processes symbols in said subchannels. 